gdz.top
Номер 374, страница 113 - гдз по алгебре 9 класс учебник Солтан, Солтан
Авторы: Солтан Г. Н., Солтан А. Е., Жумадилова А. Ж.
Тип: Учебник
Издательство: Кокшетау
Год издания: 2019 - 2026
ISBN: 978-601-317-424-2
Рекомендовано Министерством образования и науки Республики Казахстан
Популярные ГДЗ в 9 классе
III. Последовательности. 15. Арифметическая профессия и ее свойства - номер 374, страница 113.
App\Models\Task {#1024 // resources/views/models/task/default.blade.php #connection: "mysql" #table: "tasks" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 1108098 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "113" "field_page_end" => null "field_url" => "/9-klass/algebra/kokshetau-soltan-uchebnik/1-374" "field_display_title" => "374" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#331 #items: array:1 [ 0 => App\Models\Term {#1029 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 26 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "номер" "field_cases" => array:6 [ "field_accusative_case" => "номер" "field_creative_case" => "номером" "field_dative_case" => "номеру" "field_genitive_case" => "номера" "field_nominative_case" => "номер" "field_prepositional_case" => "номере" ] "field_short_name" => "№" ] #original: array:6 [ "id" => 26 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "номер" "field_cases" => array:6 [ "field_accusative_case" => "номер" "field_creative_case" => "номером" "field_dative_case" => "номеру" "field_genitive_case" => "номера" "field_nominative_case" => "номер" "field_prepositional_case" => "номере" ] "field_short_name" => "№" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1026 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#342 #items: array:1 [ 0 => App\Models\Branch {#1023 #connection: "mysql" #table: "branches" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 1107653 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "III. Последовательности" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#333 #items: [] #escapeWhenCastingToString: false } "field_page_start" => "92" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1033 #items: array:1 [ 0 => App\Models\Book {#1030 #connection: "mysql" #table: "books" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:50 [ "id" => 4298 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_tree_default_status" => "tasks" "field_pages_status" => null "field_subject" => Illuminate\Database\Eloquent\Collection {#1032 #items: array:1 [ 0 => App\Models\Term {#1034 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:10 [ "id" => 6471 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Алгебра" "field_abbreviated_name" => null "field_cases" => array:6 [ "field_accusative_case" => "алгебру" "field_creative_case" => "алгеброй" "field_dative_case" => "алгебре" "field_genitive_case" => "алгебры" "field_nominative_case" => "алгебра" "field_prepositional_case" => "алгебре" ] "field_foreign_lang_name" => null "field_short_name" => null "field_subject_type" => "technical_subject" "field_translit" => "algebra" ] #original: array:10 [ "id" => 6471 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Алгебра" "field_abbreviated_name" => null "field_cases" => array:6 [ "field_accusative_case" => "алгебру" "field_creative_case" => "алгеброй" "field_dative_case" => "алгебре" "field_genitive_case" => "алгебры" "field_nominative_case" => "алгебра" "field_prepositional_case" => "алгебре" ] "field_foreign_lang_name" => null "field_short_name" => null "field_subject_type" => "technical_subject" "field_translit" => "algebra" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_class" => Illuminate\Database\Eloquent\Collection {#1035 #items: array:1 [ 0 => App\Models\Term {#1036 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 5458 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "9" "field_cases" => array:6 [ "field_accusative_case" => "девятый" "field_creative_case" => "девятым" "field_dative_case" => "девятому" "field_genitive_case" => "девятого" "field_nominative_case" => "девятый" "field_prepositional_case" => "девятом" ] "field_translit" => "devjatyj" ] #original: array:6 [ "id" => 5458 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "9" "field_cases" => array:6 [ "field_accusative_case" => "девятый" "field_creative_case" => "девятым" "field_dative_case" => "девятому" "field_genitive_case" => "девятого" "field_nominative_case" => "девятый" "field_prepositional_case" => "девятом" ] "field_translit" => "devjatyj" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_publisher" => Illuminate\Database\Eloquent\Collection {#1037 #items: array:1 [ 0 => App\Models\Term {#1038 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 7002 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Кокшетау" "field_cases" => array:6 [ "field_accusative_case" => null "field_creative_case" => null "field_dative_case" => null "field_genitive_case" => null "field_nominative_case" => null "field_prepositional_case" => null ] "field_translit" => "Kokshetau" ] #original: array:6 [ "id" => 7002 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Кокшетау" "field_cases" => array:6 [ "field_accusative_case" => null "field_creative_case" => null "field_dative_case" => null "field_genitive_case" => null "field_nominative_case" => null "field_prepositional_case" => null ] "field_translit" => "Kokshetau" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_author" => Illuminate\Database\Eloquent\Collection {#1039 #items: array:3 [ 0 => App\Models\Term {#1040 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:12 [ "id" => 7003 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Солтан" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Генадий" "field_patronymic" => "Николаевич" "field_surname_rp" => null ] #original: array:12 [ "id" => 7003 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Солтан" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Генадий" "field_patronymic" => "Николаевич" "field_surname_rp" => null ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 1 => App\Models\Term {#1041 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:12 [ "id" => 7004 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Солтан" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Алла" "field_patronymic" => "Евгеньевна" "field_surname_rp" => null ] #original: array:12 [ "id" => 7004 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Солтан" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Алла" "field_patronymic" => "Евгеньевна" "field_surname_rp" => null ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 2 => App\Models\Term {#1042 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:12 [ "id" => 7005 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Жумадилова" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Аманбала" "field_patronymic" => "Жумадиловна" "field_surname_rp" => null ] #original: array:12 [ "id" => 7005 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Жумадилова" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Аманбала" "field_patronymic" => "Жумадиловна" "field_surname_rp" => null ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1043 #items: [] #escapeWhenCastingToString: false } "field_book_type" => Illuminate\Database\Eloquent\Collection {#1044 #items: array:1 [ 0 => App\Models\Term {#1045 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:10 [ "id" => 6671 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Учебник" "field_book_type_foreign" => null "field_cases" => array:6 [ "field_accusative_case" => "учебник" "field_creative_case" => "учебником" "field_dative_case" => "учебнику" "field_genitive_case" => "учебника" "field_nominative_case" => "учебник" "field_prepositional_case" => "учебнике" ] "field_plural_form" => null "field_short_name" => null "field_short_name_foreign" => null "field_translit" => "uchebnik" ] #original: array:10 [ "id" => 6671 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Учебник" "field_book_type_foreign" => null "field_cases" => array:6 [ "field_accusative_case" => "учебник" "field_creative_case" => "учебником" "field_dative_case" => "учебнику" "field_genitive_case" => "учебника" "field_nominative_case" => "учебник" "field_prepositional_case" => "учебнике" ] "field_plural_form" => null "field_short_name" => null "field_short_name_foreign" => null "field_translit" => "uchebnik" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_country" => Illuminate\Database\Eloquent\Collection {#1046 #items: array:1 [ 0 => App\Models\Term {#1047 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 6994 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Казахстан" "field_cases" => array:6 [ "field_accusative_case" => null "field_creative_case" => null "field_dative_case" => null "field_genitive_case" => null "field_nominative_case" => null "field_prepositional_case" => null ] "field_translit" => "kazakhstan" ] #original: array:6 [ "id" => 6994 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Казахстан" "field_cases" => array:6 [ "field_accusative_case" => null "field_creative_case" => null "field_dative_case" => null "field_genitive_case" => null "field_nominative_case" => null "field_prepositional_case" => null ] "field_translit" => "kazakhstan" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_city" => Illuminate\Database\Eloquent\Collection {#1048 #items: array:1 [ 0 => App\Models\Term {#1049 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 6995 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Алматы" "field_cases" => array:6 [ "field_accusative_case" => null "field_creative_case" => null "field_dative_case" => null "field_genitive_case" => null "field_nominative_case" => null "field_prepositional_case" => null ] "field_translit" => "almaty" ] #original: array:6 [ "id" => 6995 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Алматы" "field_cases" => array:6 [ "field_accusative_case" => null "field_creative_case" => null "field_dative_case" => null "field_genitive_case" => null "field_nominative_case" => null "field_prepositional_case" => null ] "field_translit" => "almaty" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_series" => Illuminate\Database\Eloquent\Collection {#1050 #items: [] #escapeWhenCastingToString: false } "field_umk" => Illuminate\Database\Eloquent\Collection {#1051 #items: [] #escapeWhenCastingToString: false } "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1052 #items: [] #escapeWhenCastingToString: false } "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1053 #items: [] #escapeWhenCastingToString: false } "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1054 #items: [] #escapeWhenCastingToString: false } "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1055 #items: [] #escapeWhenCastingToString: false } "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2019" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Учебник для учащихся 9 класса общеобразовательных школ" "field_allowed" => "Рекомендовано Министерством образования и науки Республики Казахстан" "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "1291" "field_priority" => "4" "field_default_folder" => "/algebra_09/soltan-u19/" "field_isbn" => "978-601-317-424-2" "field_cover" => array:1 [ 0 => "/media/algebra_09/soltan-u19/covers/cover1.webp?ts=1752140452" ] "field_cover_alts" => array:1 [ 0 => "" ] "field_covers" => array:1 [ 0 => array:4 [ "path" => "/media/algebra_09/soltan-u19/covers/cover1.webp?ts=1752140452" "alt" => "" "width" => "1940" "height" => "2895" ] ] "field_popular_book" => null "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1056 #items: [] #escapeWhenCastingToString: false } "field_new_book" => Illuminate\Database\Eloquent\Collection {#1057 #items: [] #escapeWhenCastingToString: false } "field_old_book" => Illuminate\Database\Eloquent\Collection {#1058 #items: [] #escapeWhenCastingToString: false } "field_url" => "/9-klass/algebra/kokshetau-soltan-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1059 #items: [] #escapeWhenCastingToString: false } "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ "class" => 380 "subject" => 542 "class_subject" => 386 ] ] #original: array:50 [ "id" => 4298 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_tree_default_status" => "tasks" "field_pages_status" => null "field_subject" => Illuminate\Database\Eloquent\Collection {#1032} "field_class" => Illuminate\Database\Eloquent\Collection {#1035} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1037} "field_author" => Illuminate\Database\Eloquent\Collection {#1039} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1043} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1044} "field_country" => Illuminate\Database\Eloquent\Collection {#1046} "field_city" => Illuminate\Database\Eloquent\Collection {#1048} "field_series" => Illuminate\Database\Eloquent\Collection {#1050} "field_umk" => Illuminate\Database\Eloquent\Collection {#1051} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1052} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1053} "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1054} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1055} "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2019" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Учебник для учащихся 9 класса общеобразовательных школ" "field_allowed" => "Рекомендовано Министерством образования и науки Республики Казахстан" "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "1291" "field_priority" => "4" "field_default_folder" => "/algebra_09/soltan-u19/" "field_isbn" => "978-601-317-424-2" "field_cover" => array:1 [ 0 => "/media/algebra_09/soltan-u19/covers/cover1.webp?ts=1752140452" ] "field_cover_alts" => array:1 [ 0 => "" ] "field_covers" => array:1 [ 0 => array:4 [ "path" => "/media/algebra_09/soltan-u19/covers/cover1.webp?ts=1752140452" "alt" => "" "width" => "1940" "height" => "2895" ] ] "field_popular_book" => null "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1056} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1057} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1058} "field_url" => "/9-klass/algebra/kokshetau-soltan-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1059} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ "class" => 380 "subject" => 542 "class_subject" => 386 ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1060 #items: [] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1107653 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "III. Последовательности" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#333} "field_page_start" => "92" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1033} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1060} ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "parent_branches" => Illuminate\Database\Eloquent\Collection {#1061 #items: array:2 [ 0 => App\Models\Branch {#1023} 1 => App\Models\Branch {#1062 #connection: "mysql" #table: "branches" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 1107656 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "15. Арифметическая профессия и ее свойства" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1063 #items: [] #escapeWhenCastingToString: false } "field_page_start" => "108" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1064 #items: array:1 [ 0 => App\Models\Book {#1030} ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1065 #items: array:1 [ 0 => App\Models\Branch {#1066 #connection: "mysql" #table: "branches" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 1107653 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "III. Последовательности" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1067 #items: [] #escapeWhenCastingToString: false } "field_page_start" => "92" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1068 #items: array:1 [ 0 => App\Models\Book {#1069 …30} ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1097 #items: [] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1107653 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "III. Последовательности" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1067} "field_page_start" => "92" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1068} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1097} ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1107656 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "15. Арифметическая профессия и ее свойства" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1063} "field_page_start" => "108" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1064} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1065} ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1098 #items: array:3 [ 0 => App\Models\Element {#1099 #connection: "mysql" #table: "elements" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:7 [ "id" => 1276729 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1100 #items: array:1 [ 0 => App\Models\Edition {#1101 #connection: "mysql" #table: "editions" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:21 [ "id" => 4953 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Условие" "field_order" => "1" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1102 #items: array:1 [ 0 => App\Models\Term {#1103 …30} ] #escapeWhenCastingToString: false } "field_content_type" => "free" "field_content_mode" => "text, image" "field_page_content_mode" => "image" "field_content_text_checked" => null "field_page_content_text_checked" => "0" "field_solution_author" => "Автор" "field_moderator" => "pasha" "field_edition_type" => "statement" "field_root_dir" => "0-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1104 #items: [] #escapeWhenCastingToString: false } "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1105 #items: [] #escapeWhenCastingToString: false } "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1106 #items: [] #escapeWhenCastingToString: false } "field_content_source" => null ] #original: array:21 [ "id" => 4953 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Условие" "field_order" => "1" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1102} "field_content_type" => "free" "field_content_mode" => "text, image" "field_page_content_mode" => "image" "field_content_text_checked" => null "field_page_content_text_checked" => "0" "field_solution_author" => "Автор" "field_moderator" => "pasha" "field_edition_type" => "statement" "field_root_dir" => "0-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1104} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1105} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1106} "field_content_source" => null ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "task" => array:2 [ "refs" => "1108098" "type" => "task" ] "text" => "<p><strong>374.</strong> Является ли арифметической прогрессией последовательность, график которой изображен на рисунке 37, а, б? Если является, то запишите формулу ее $n$-го члена.</p><p><strong>а)</strong></p><svg viewBox="0 0 80 95" xmlns="http://www.w3.org/2000/svg"><!-- Grid lines --><line x1="10" y1="85" x2="70" y2="85" stroke="lightgray" stroke-width="0.5" /><line x1="10" y1="75" x2="70" y2="75" stroke="lightgray" stroke-width="0.5" /><line x1="10" y1="65" x2="70" y2="65" stroke="lightgray" stroke-width="0.5" /><line x1="10" y1="55" x2="70" y2="55" stroke="lightgray" stroke-width="0.5" /><line x1="10" y1="45" x2="70" y2="45" stroke="lightgray" stroke-width="0.5" /><line x1="10" y1="35" x2="70" y2="35" stroke="lightgray" stroke-width="0.5" /><line x1="10" y1="25" x2="70" y2="25" stroke="lightgray" stroke-width="0.5" /><line x1="10" y1="15" x2="70" y2="15" stroke="lightgray" stroke-width="0.5" /><line x1="10" y1="15" x2="10" y2="85" stroke="lightgray" stroke-width="0.5" /><line x1="20" y1="15" x2="20" y2="85" stroke="lightgray" stroke-width="0.5" /><line x1="30" y1="15" x2="30" y2="85" stroke="lightgray" stroke-width="0.5" /><line x1="40" y1="15" x2="40" y2="85" stroke="lightgray" stroke-width="0.5" /><line x1="50" y1="15" x2="50" y2="85" stroke="lightgray" stroke-width="0.5" /><line x1="60" y1="15" x2="60" y2="85" stroke="lightgray" stroke-width="0.5" /><line x1="70" y1="15" x2="70" y2="85" stroke="lightgray" stroke-width="0.5" /><!-- Axes --><line x1="10" y1="15" x2="10" y2="85" stroke="black" stroke-width="1" /><line x1="10" y1="85" x2="70" y2="85" stroke="black" stroke-width="1" /><!-- Arrows --><polyline points="10,15 7,20 13,20 10,15" fill="black" /><polyline points="70,85 65,82 65,88 70,85" fill="black" /><!-- Labels --><text x="5" y="10" font-size="8" text-anchor="middle">y</text><text x="75" y="90" font-size="8" text-anchor="middle">x</text><text x="5" y="90" font-size="8" text-anchor="middle">O</text><!-- Tick labels X-axis --><text x="20" y="90" font-size="8" text-anchor="middle">1</text><text x="30" y="90" font-size="8" text-anchor="middle">2</text><text x="40" y="90" font-size="8" text-anchor="middle">3</text><text x="50" y="90" font-size="8" text-anchor="middle">4</text><text x="60" y="90" font-size="8" text-anchor="middle">5</text><text x="70" y="90" font-size="8" text-anchor="middle">6</text><!-- Tick labels Y-axis --><text x="0" y="77" font-size="8" text-anchor="end">1</text><text x="0" y="67" font-size="8" text-anchor="end">2</text><text x="0" y="57" font-size="8" text-anchor="end">3</text><text x="0" y="47" font-size="8" text-anchor="end">4</text><text x="0" y="37" font-size="8" text-anchor="end">5</text><text x="0" y="27" font-size="8" text-anchor="end">6</text><text x="0" y="17" font-size="8" text-anchor="end">7</text><!-- Points for graph a) --><circle cx="20" cy="15" r="1.5" fill="black" /><circle cx="30" cy="35" r="1.5" fill="black" /><circle cx="40" cy="45" r="1.5" fill="black" /><circle cx="50" cy="58" r="1.5" fill="black" /><circle cx="60" cy="70" r="1.5" fill="black" /><circle cx="70" cy="80" r="1.5" fill="black" /></svg><p><strong>б)</strong></p><svg viewBox="0 0 80 95" xmlns="http://www.w3.org/2000/svg"><!-- Grid lines --><line x1="10" y1="85" x2="70" y2="85" stroke="lightgray" stroke-width="0.5" /><line x1="10" y1="75" x2="70" y2="75" stroke="lightgray" stroke-width="0.5" /><line x1="10" y1="65" x2="70" y2="65" stroke="lightgray" stroke-width="0.5" /><line x1="10" y1="55" x2="70" y2="55" stroke="lightgray" stroke-width="0.5" /><line x1="10" y1="45" x2="70" y2="45" stroke="lightgray" stroke-width="0.5" /><line x1="10" y1="35" x2="70" y2="35" stroke="lightgray" stroke-width="0.5" /><line x1="10" y1="25" x2="70" y2="25" stroke="lightgray" stroke-width="0.5" /><line x1="10" y1="15" x2="70" y2="15" stroke="lightgray" stroke-width="0.5" /><line x1="10" y1="15" x2="10" y2="85" stroke="lightgray" stroke-width="0.5" /><line x1="20" y1="15" x2="20" y2="85" stroke="lightgray" stroke-width="0.5" /><line x1="30" y1="15" x2="30" y2="85" stroke="lightgray" stroke-width="0.5" /><line x1="40" y1="15" x2="40" y2="85" stroke="lightgray" stroke-width="0.5" /><line x1="50" y1="15" x2="50" y2="85" stroke="lightgray" stroke-width="0.5" /><line x1="60" y1="15" x2="60" y2="85" stroke="lightgray" stroke-width="0.5" /><line x1="70" y1="15" x2="70" y2="85" stroke="lightgray" stroke-width="0.5" /><!-- Axes --><line x1="10" y1="15" x2="10" y2="85" stroke="black" stroke-width="1" /><line x1="10" y1="85" x2="70" y2="85" stroke="black" stroke-width="1" /><!-- Arrows --><polyline points="10,15 7,20 13,20 10,15" fill="black" /><polyline points="70,85 65,82 65,88 70,85" fill="black" /><!-- Labels --><text x="5" y="10" font-size="8" text-anchor="middle">y</text><text x="75" y="90" font-size="8" text-anchor="middle">x</text><text x="5" y="90" font-size="8" text-anchor="middle">O</text><!-- Tick labels X-axis --><text x="20" y="90" font-size="8" text-anchor="middle">1</text><text x="30" y="90" font-size="8" text-anchor="middle">2</text><text x="40" y="90" font-size="8" text-anchor="middle">3</text><text x="50" y="90" font-size="8" text-anchor="middle">4</text><text x="60" y="90" font-size="8" text-anchor="middle">5</text><text x="70" y="90" font-size="8" text-anchor="middle">6</text><!-- Tick labels Y-axis --><text x="0" y="77" font-size="8" text-anchor="end">1</text><text x="0" y="67" font-size="8" text-anchor="end">2</text><text x="0" y="57" font-size="8" text-anchor="end">3</text><text x="0" y="47" font-size="8" text-anchor="end">4</text><text x="0" y="37" font-size="8" text-anchor="end">5</text><text x="0" y="27" font-size="8" text-anchor="end">6</text><text x="0" y="17" font-size="8" text-anchor="end">7</text><!-- Points for graph b) --><circle cx="20" cy="25" r="1.5" fill="black" /><circle cx="30" cy="45" r="1.5" fill="black" /><circle cx="40" cy="65" r="1.5" fill="black" /><circle cx="60" cy="65" r="1.5" fill="black" /><circle cx="70" cy="65" r="1.5" fill="black" /></svg><p>Рисунок 37</p>" "img" => array:1 [ 0 => array:5 [ "name" => "374-1.jpg" "alt" => null "width" => "1555" "height" => 859 "path" => "/media/algebra_09/soltan-u19/0-1/374-1.webp?ts=1752834398" ] ] ] #original: array:7 [ "id" => 1276729 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1100} "task" => array:2 [ "refs" => "1108098" "type" => "task" ] "text" => "<p><strong>374.</strong> Является ли арифметической прогрессией последовательность, график которой изображен на рисунке 37, а, б? Если является, то запишите формулу ее $n$-го члена.</p><p><strong>а)</strong></p><svg viewBox="0 0 80 95" xmlns="http://www.w3.org/2000/svg"><!-- Grid lines --><line x1="10" y1="85" x2="70" y2="85" stroke="lightgray" stroke-width="0.5" /><line x1="10" y1="75" x2="70" y2="75" stroke="lightgray" stroke-width="0.5" /><line x1="10" y1="65" x2="70" y2="65" stroke="lightgray" stroke-width="0.5" /><line x1="10" y1="55" x2="70" y2="55" stroke="lightgray" stroke-width="0.5" /><line x1="10" y1="45" x2="70" y2="45" stroke="lightgray" stroke-width="0.5" /><line x1="10" y1="35" x2="70" y2="35" stroke="lightgray" stroke-width="0.5" /><line x1="10" y1="25" x2="70" y2="25" stroke="lightgray" stroke-width="0.5" /><line x1="10" y1="15" x2="70" y2="15" stroke="lightgray" stroke-width="0.5" /><line x1="10" y1="15" x2="10" y2="85" stroke="lightgray" stroke-width="0.5" /><line x1="20" y1="15" x2="20" y2="85" stroke="lightgray" stroke-width="0.5" /><line x1="30" y1="15" x2="30" y2="85" stroke="lightgray" stroke-width="0.5" /><line x1="40" y1="15" x2="40" y2="85" stroke="lightgray" stroke-width="0.5" /><line x1="50" y1="15" x2="50" y2="85" stroke="lightgray" stroke-width="0.5" /><line x1="60" y1="15" x2="60" y2="85" stroke="lightgray" stroke-width="0.5" /><line x1="70" y1="15" x2="70" y2="85" stroke="lightgray" stroke-width="0.5" /><!-- Axes --><line x1="10" y1="15" x2="10" y2="85" stroke="black" stroke-width="1" /><line x1="10" y1="85" x2="70" y2="85" stroke="black" stroke-width="1" /><!-- Arrows --><polyline points="10,15 7,20 13,20 10,15" fill="black" /><polyline points="70,85 65,82 65,88 70,85" fill="black" /><!-- Labels --><text x="5" y="10" font-size="8" text-anchor="middle">y</text><text x="75" y="90" font-size="8" text-anchor="middle">x</text><text x="5" y="90" font-size="8" text-anchor="middle">O</text><!-- Tick labels X-axis --><text x="20" y="90" font-size="8" text-anchor="middle">1</text><text x="30" y="90" font-size="8" text-anchor="middle">2</text><text x="40" y="90" font-size="8" text-anchor="middle">3</text><text x="50" y="90" font-size="8" text-anchor="middle">4</text><text x="60" y="90" font-size="8" text-anchor="middle">5</text><text x="70" y="90" font-size="8" text-anchor="middle">6</text><!-- Tick labels Y-axis --><text x="0" y="77" font-size="8" text-anchor="end">1</text><text x="0" y="67" font-size="8" text-anchor="end">2</text><text x="0" y="57" font-size="8" text-anchor="end">3</text><text x="0" y="47" font-size="8" text-anchor="end">4</text><text x="0" y="37" font-size="8" text-anchor="end">5</text><text x="0" y="27" font-size="8" text-anchor="end">6</text><text x="0" y="17" font-size="8" text-anchor="end">7</text><!-- Points for graph a) --><circle cx="20" cy="15" r="1.5" fill="black" /><circle cx="30" cy="35" r="1.5" fill="black" /><circle cx="40" cy="45" r="1.5" fill="black" /><circle cx="50" cy="58" r="1.5" fill="black" /><circle cx="60" cy="70" r="1.5" fill="black" /><circle cx="70" cy="80" r="1.5" fill="black" /></svg><p><strong>б)</strong></p><svg viewBox="0 0 80 95" xmlns="http://www.w3.org/2000/svg"><!-- Grid lines --><line x1="10" y1="85" x2="70" y2="85" stroke="lightgray" stroke-width="0.5" /><line x1="10" y1="75" x2="70" y2="75" stroke="lightgray" stroke-width="0.5" /><line x1="10" y1="65" x2="70" y2="65" stroke="lightgray" stroke-width="0.5" /><line x1="10" y1="55" x2="70" y2="55" stroke="lightgray" stroke-width="0.5" /><line x1="10" y1="45" x2="70" y2="45" stroke="lightgray" stroke-width="0.5" /><line x1="10" y1="35" x2="70" y2="35" stroke="lightgray" stroke-width="0.5" /><line x1="10" y1="25" x2="70" y2="25" stroke="lightgray" stroke-width="0.5" /><line x1="10" y1="15" x2="70" y2="15" stroke="lightgray" stroke-width="0.5" /><line x1="10" y1="15" x2="10" y2="85" stroke="lightgray" stroke-width="0.5" /><line x1="20" y1="15" x2="20" y2="85" stroke="lightgray" stroke-width="0.5" /><line x1="30" y1="15" x2="30" y2="85" stroke="lightgray" stroke-width="0.5" /><line x1="40" y1="15" x2="40" y2="85" stroke="lightgray" stroke-width="0.5" /><line x1="50" y1="15" x2="50" y2="85" stroke="lightgray" stroke-width="0.5" /><line x1="60" y1="15" x2="60" y2="85" stroke="lightgray" stroke-width="0.5" /><line x1="70" y1="15" x2="70" y2="85" stroke="lightgray" stroke-width="0.5" /><!-- Axes --><line x1="10" y1="15" x2="10" y2="85" stroke="black" stroke-width="1" /><line x1="10" y1="85" x2="70" y2="85" stroke="black" stroke-width="1" /><!-- Arrows --><polyline points="10,15 7,20 13,20 10,15" fill="black" /><polyline points="70,85 65,82 65,88 70,85" fill="black" /><!-- Labels --><text x="5" y="10" font-size="8" text-anchor="middle">y</text><text x="75" y="90" font-size="8" text-anchor="middle">x</text><text x="5" y="90" font-size="8" text-anchor="middle">O</text><!-- Tick labels X-axis --><text x="20" y="90" font-size="8" text-anchor="middle">1</text><text x="30" y="90" font-size="8" text-anchor="middle">2</text><text x="40" y="90" font-size="8" text-anchor="middle">3</text><text x="50" y="90" font-size="8" text-anchor="middle">4</text><text x="60" y="90" font-size="8" text-anchor="middle">5</text><text x="70" y="90" font-size="8" text-anchor="middle">6</text><!-- Tick labels Y-axis --><text x="0" y="77" font-size="8" text-anchor="end">1</text><text x="0" y="67" font-size="8" text-anchor="end">2</text><text x="0" y="57" font-size="8" text-anchor="end">3</text><text x="0" y="47" font-size="8" text-anchor="end">4</text><text x="0" y="37" font-size="8" text-anchor="end">5</text><text x="0" y="27" font-size="8" text-anchor="end">6</text><text x="0" y="17" font-size="8" text-anchor="end">7</text><!-- Points for graph b) --><circle cx="20" cy="25" r="1.5" fill="black" /><circle cx="30" cy="45" r="1.5" fill="black" /><circle cx="40" cy="65" r="1.5" fill="black" /><circle cx="60" cy="65" r="1.5" fill="black" /><circle cx="70" cy="65" r="1.5" fill="black" /></svg><p>Рисунок 37</p>" "img" => array:1 [ 0 => array:5 [ "name" => "374-1.jpg" "alt" => null "width" => "1555" "height" => 859 "path" => "/media/algebra_09/soltan-u19/0-1/374-1.webp?ts=1752834398" ] ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 1 => App\Models\Element {#1107 #connection: "mysql" #table: "elements" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 1278020 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1108 #items: array:1 [ 0 => App\Models\Edition {#1109 #connection: "mysql" #table: "editions" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:21 [ "id" => 4954 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение" "field_order" => "2" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1110 #items: array:1 [ 0 => App\Models\Term {#1111 …30} ] #escapeWhenCastingToString: false } "field_content_type" => "free" "field_content_mode" => "image" "field_page_content_mode" => "" "field_content_text_checked" => "0" "field_page_content_text_checked" => "0" "field_solution_author" => "Неизвестный" "field_moderator" => "pasha" "field_edition_type" => "solution" "field_root_dir" => "1-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1112 #items: [] #escapeWhenCastingToString: false } "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1113 #items: [] #escapeWhenCastingToString: false } "field_process_formula" => "" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1114 #items: [] #escapeWhenCastingToString: false } "field_content_source" => null ] #original: array:21 [ "id" => 4954 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение" "field_order" => "2" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1110} "field_content_type" => "free" "field_content_mode" => "image" "field_page_content_mode" => "" "field_content_text_checked" => "0" "field_page_content_text_checked" => "0" "field_solution_author" => "Неизвестный" "field_moderator" => "pasha" "field_edition_type" => "solution" "field_root_dir" => "1-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1112} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1113} "field_process_formula" => "" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1114} "field_content_source" => null ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "task" => array:2 [ "refs" => "1108098" "type" => "task" ] "img" => array:1 [ 0 => array:5 [ "name" => "374-1.jpg" "alt" => null "width" => "922" "height" => 470 "path" => "/media/algebra_09/soltan-u19/1-1/374-1.webp?ts=1752831112" ] ] ] #original: array:6 [ "id" => 1278020 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1108} "task" => array:2 [ "refs" => "1108098" "type" => "task" ] "img" => array:1 [ 0 => array:5 [ "name" => "374-1.jpg" "alt" => null "width" => "922" "height" => 470 "path" => "/media/algebra_09/soltan-u19/1-1/374-1.webp?ts=1752831112" ] ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 2 => App\Models\Element {#1115 #connection: "mysql" #table: "elements" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 1553975 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1116 #items: array:1 [ 0 => App\Models\Edition {#1117 #connection: "mysql" #table: "editions" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:21 [ "id" => 5665 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение 2 (rus)" "field_order" => "3" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1118 #items: array:1 [ 0 => App\Models\Term {#1119 …30} ] #escapeWhenCastingToString: false } "field_content_type" => "free" "field_content_mode" => "text" "field_page_content_mode" => "" "field_content_text_checked" => null "field_page_content_text_checked" => "0" "field_solution_author" => "Gemini 2.5 Pro" "field_moderator" => "tolik" "field_edition_type" => "solution" "field_root_dir" => "2-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1120 #items: [] #escapeWhenCastingToString: false } "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1121 #items: [] #escapeWhenCastingToString: false } "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1122 #items: [] #escapeWhenCastingToString: false } "field_content_source" => null ] #original: array:21 [ "id" => 5665 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение 2 (rus)" "field_order" => "3" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1118} "field_content_type" => "free" "field_content_mode" => "text" "field_page_content_mode" => "" "field_content_text_checked" => null "field_page_content_text_checked" => "0" "field_solution_author" => "Gemini 2.5 Pro" "field_moderator" => "tolik" "field_edition_type" => "solution" "field_root_dir" => "2-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1120} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1121} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1122} "field_content_source" => null ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "task" => array:2 [ "refs" => "1108098" "type" => "task" ] "text" => "<p><strong>а)</strong></p><p>Арифметическая прогрессия — это числовая последовательность, каждый член которой, начиная со второго, равен предыдущему, сложенному с одним и тем же числом, называемым разностью прогрессии (<i>d</i>). Чтобы определить, является ли последовательность на графике арифметической прогрессией, найдем её члены и проверим, постоянна ли разность между ними.</p><p>По графику на рисунке 37, а) определим первые несколько членов последовательности $a_n$, где <i>n</i> — номер члена (ось <i>x</i>), а $a_n$ — его значение (ось <i>y</i>):</p><p>$a_1 = 7$</p><p>$a_2 = 5,5$</p><p>$a_3 = 4$</p><p>$a_4 = 2,5$</p><p>$a_5 = 1$</p><p>Теперь найдем разность <i>d</i> между соседними членами:</p><p>$d_1 = a_2 - a_1 = 5,5 - 7 = -1,5$</p><p>$d_2 = a_3 - a_2 = 4 - 5,5 = -1,5$</p><p>$d_3 = a_4 - a_3 = 2,5 - 4 = -1,5$</p><p>$d_4 = a_5 - a_4 = 1 - 2,5 = -1,5$</p><p>Так как разность между всеми последовательными членами постоянна и равна -1,5, данная последовательность является арифметической прогрессией. Первый член прогрессии $a_1 = 7$, а её разность $d = -1,5$.</p><p>Запишем формулу <i>n</i>-го члена арифметической прогрессии: $a_n = a_1 + (n-1)d$.</p><p>Подставим найденные значения $a_1$ и <i>d</i>:</p><p>$a_n = 7 + (n-1) \cdot (-1,5)$</p><p>Упростим выражение:</p><p>$a_n = 7 - 1,5n + 1,5$</p><p>$a_n = 8,5 - 1,5n$</p><p><strong>Ответ:</strong> Да, является. Формула <i>n</i>-го члена: $a_n = 8,5 - 1,5n$.</p><br><p><strong>б)</strong></p><p>Аналогично проанализируем график на рисунке 37, б). Определим первые несколько членов последовательности:</p><p>$a_1 = 6$</p><p>$a_2 = 4$</p><p>$a_3 = 4$</p><p>$a_4 = 2$</p><p>$a_5 = 2$</p><p>Теперь найдем разность между соседними членами:</p><p>$d_1 = a_2 - a_1 = 4 - 6 = -2$</p><p>$d_2 = a_3 - a_2 = 4 - 4 = 0$</p><p>Разности между соседними членами не равны ($-2 \neq 0$). Следовательно, эта последовательность не является арифметической прогрессией, так как у неё нет постоянной разности.</p><p><strong>Ответ:</strong> Нет, не является.</p>" ] #original: array:6 [ "id" => 1553975 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1116} "task" => array:2 [ "refs" => "1108098" "type" => "task" ] "text" => "<p><strong>а)</strong></p><p>Арифметическая прогрессия — это числовая последовательность, каждый член которой, начиная со второго, равен предыдущему, сложенному с одним и тем же числом, называемым разностью прогрессии (<i>d</i>). Чтобы определить, является ли последовательность на графике арифметической прогрессией, найдем её члены и проверим, постоянна ли разность между ними.</p><p>По графику на рисунке 37, а) определим первые несколько членов последовательности $a_n$, где <i>n</i> — номер члена (ось <i>x</i>), а $a_n$ — его значение (ось <i>y</i>):</p><p>$a_1 = 7$</p><p>$a_2 = 5,5$</p><p>$a_3 = 4$</p><p>$a_4 = 2,5$</p><p>$a_5 = 1$</p><p>Теперь найдем разность <i>d</i> между соседними членами:</p><p>$d_1 = a_2 - a_1 = 5,5 - 7 = -1,5$</p><p>$d_2 = a_3 - a_2 = 4 - 5,5 = -1,5$</p><p>$d_3 = a_4 - a_3 = 2,5 - 4 = -1,5$</p><p>$d_4 = a_5 - a_4 = 1 - 2,5 = -1,5$</p><p>Так как разность между всеми последовательными членами постоянна и равна -1,5, данная последовательность является арифметической прогрессией. Первый член прогрессии $a_1 = 7$, а её разность $d = -1,5$.</p><p>Запишем формулу <i>n</i>-го члена арифметической прогрессии: $a_n = a_1 + (n-1)d$.</p><p>Подставим найденные значения $a_1$ и <i>d</i>:</p><p>$a_n = 7 + (n-1) \cdot (-1,5)$</p><p>Упростим выражение:</p><p>$a_n = 7 - 1,5n + 1,5$</p><p>$a_n = 8,5 - 1,5n$</p><p><strong>Ответ:</strong> Да, является. Формула <i>n</i>-го члена: $a_n = 8,5 - 1,5n$.</p><br><p><strong>б)</strong></p><p>Аналогично проанализируем график на рисунке 37, б). Определим первые несколько членов последовательности:</p><p>$a_1 = 6$</p><p>$a_2 = 4$</p><p>$a_3 = 4$</p><p>$a_4 = 2$</p><p>$a_5 = 2$</p><p>Теперь найдем разность между соседними членами:</p><p>$d_1 = a_2 - a_1 = 4 - 6 = -2$</p><p>$d_2 = a_3 - a_2 = 4 - 4 = 0$</p><p>Разности между соседними членами не равны ($-2 \neq 0$). Следовательно, эта последовательность не является арифметической прогрессией, так как у неё нет постоянной разности.</p><p><strong>Ответ:</strong> Нет, не является.</p>" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "1108099" "type" => "task" ] "previous" => array:2 [ "refs" => "1108097" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1123 #items: array:1 [ 0 => App\Models\Book {#1030} ] #escapeWhenCastingToString: false } "page" => Illuminate\Database\Eloquent\Collection {#1304 #items: array:1 [ 0 => App\Models\BookPage {#1127 #connection: "mysql" #table: "book_pages" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:21 [ "id" => 1097855 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "113" "field_url" => "/9-klass/algebra/kokshetau-soltan-uchebnik/page-113" "field_display_title" => "113" "field_folder" => "folder1" "field_image_name" => "113" "field_branch_parent" => Illuminate\Database\Eloquent\Collection {#1131 #items: [] #escapeWhenCastingToString: false } "field_weight" => "0" "field_book_parent" => Illuminate\Database\Eloquent\Collection {#1130 #items: array:1 [ 0 => App\Models\Book {#1132 #connection: "mysql" #table: "books" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:50 [ "id" => 4298 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_tree_default_status" => "tasks" "field_pages_status" => null "field_subject" => Illuminate\Database\Eloquent\Collection {#1133 #items: array:1 [ 0 => App\Models\Term {#1134 …30} ] #escapeWhenCastingToString: false } "field_class" => Illuminate\Database\Eloquent\Collection {#1135 #items: array:1 [ 0 => App\Models\Term {#1136 …30} ] #escapeWhenCastingToString: false } "field_publisher" => Illuminate\Database\Eloquent\Collection {#1137 #items: array:1 [ 0 => App\Models\Term {#1138 …30} ] #escapeWhenCastingToString: false } "field_author" => Illuminate\Database\Eloquent\Collection {#1139 #items: array:3 [ 0 => App\Models\Term {#1140 …30} 1 => App\Models\Term {#1141 …30} 2 => App\Models\Term {#1142 …30} ] #escapeWhenCastingToString: false } "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1143 #items: [] #escapeWhenCastingToString: false } "field_book_type" => Illuminate\Database\Eloquent\Collection {#1144 #items: array:1 [ 0 => App\Models\Term {#1145 …30} ] #escapeWhenCastingToString: false } "field_country" => Illuminate\Database\Eloquent\Collection {#1146 #items: array:1 [ 0 => App\Models\Term {#1147 …30} ] #escapeWhenCastingToString: false } "field_city" => Illuminate\Database\Eloquent\Collection {#1148 #items: array:1 [ 0 => App\Models\Term {#1149 …30} ] #escapeWhenCastingToString: false } "field_series" => Illuminate\Database\Eloquent\Collection {#1150 #items: [] #escapeWhenCastingToString: false } "field_umk" => Illuminate\Database\Eloquent\Collection {#1151 #items: [] #escapeWhenCastingToString: false } "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1152 #items: [] #escapeWhenCastingToString: false } "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1153 #items: [] #escapeWhenCastingToString: false } "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1154 #items: [] #escapeWhenCastingToString: false } "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1155 #items: [] #escapeWhenCastingToString: false } "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2019" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Учебник для учащихся 9 класса общеобразовательных школ" "field_allowed" => "Рекомендовано Министерством образования и науки Республики Казахстан" "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "1291" "field_priority" => "4" "field_default_folder" => "/algebra_09/soltan-u19/" "field_isbn" => "978-601-317-424-2" "field_cover" => array:1 [ 0 => "/media/algebra_09/soltan-u19/covers/cover1.webp?ts=1752140452" ] "field_cover_alts" => array:1 [ 0 => "" ] "field_covers" => array:1 [ 0 => array:4 [ "path" => "/media/algebra_09/soltan-u19/covers/cover1.webp?ts=1752140452" "alt" => "" "width" => "1940" "height" => "2895" ] ] "field_popular_book" => null "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1156 #items: [] #escapeWhenCastingToString: false } "field_new_book" => Illuminate\Database\Eloquent\Collection {#1157 #items: [] #escapeWhenCastingToString: false } "field_old_book" => Illuminate\Database\Eloquent\Collection {#1158 #items: [] #escapeWhenCastingToString: false } "field_url" => "/9-klass/algebra/kokshetau-soltan-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1159 #items: [] #escapeWhenCastingToString: false } "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ "class" => 380 "subject" => 542 "class_subject" => 386 ] ] #original: array:50 [ "id" => 4298 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_tree_default_status" => "tasks" "field_pages_status" => null "field_subject" => Illuminate\Database\Eloquent\Collection {#1133} "field_class" => Illuminate\Database\Eloquent\Collection {#1135} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1137} "field_author" => Illuminate\Database\Eloquent\Collection {#1139} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1143} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1144} "field_country" => Illuminate\Database\Eloquent\Collection {#1146} "field_city" => Illuminate\Database\Eloquent\Collection {#1148} "field_series" => Illuminate\Database\Eloquent\Collection {#1150} "field_umk" => Illuminate\Database\Eloquent\Collection {#1151} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1152} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1153} "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1154} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1155} "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2019" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Учебник для учащихся 9 класса общеобразовательных школ" "field_allowed" => "Рекомендовано Министерством образования и науки Республики Казахстан" "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "1291" "field_priority" => "4" "field_default_folder" => "/algebra_09/soltan-u19/" "field_isbn" => "978-601-317-424-2" "field_cover" => array:1 [ 0 => "/media/algebra_09/soltan-u19/covers/cover1.webp?ts=1752140452" ] "field_cover_alts" => array:1 [ 0 => "" ] "field_covers" => array:1 [ 0 => array:4 [ "path" => "/media/algebra_09/soltan-u19/covers/cover1.webp?ts=1752140452" "alt" => "" "width" => "1940" "height" => "2895" ] ] "field_popular_book" => null "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1156} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1157} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1158} "field_url" => "/9-klass/algebra/kokshetau-soltan-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1159} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ "class" => 380 "subject" => 542 "class_subject" => 386 ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "edition_groups" => Illuminate\Database\Eloquent\Collection {#1160 #items: [] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1161 #items: array:1 [ 0 => App\Models\Element {#1162 #connection: "mysql" #table: "elements" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 1261006 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1163 #items: array:1 [ 0 => App\Models\Edition {#1164 …30} ] #escapeWhenCastingToString: false } "book_page" => array:2 [ "refs" => "1097855" "type" => "book_page" ] "img" => array:1 [ 0 => array:5 [ "name" => "113-1.jpg" "alt" => null "width" => "2009" "height" => 2972 "path" => "/media/algebra_09/soltan-u19/0-folder1/113-1.webp?ts=1752141155" ] ] ] #original: array:6 [ "id" => 1261006 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1163} "book_page" => array:2 [ "refs" => "1097855" "type" => "book_page" ] "img" => array:1 [ 0 => array:5 [ "name" => "113-1.jpg" "alt" => null "width" => "2009" "height" => 2972 "path" => "/media/algebra_09/soltan-u19/0-folder1/113-1.webp?ts=1752141155" ] ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "1097856" "type" => "book_page" ] "previous" => array:2 [ "refs" => "1097854" "type" => "book_page" ] "tasks" => Illuminate\Database\Eloquent\Collection {#1170 #items: array:6 [ 0 => App\Models\Task {#1171 #connection: "mysql" #table: "tasks" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 1108094 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "113" "field_page_end" => null "field_url" => "/9-klass/algebra/kokshetau-soltan-uchebnik/1-370" "field_display_title" => "370" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1172 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1174 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1175 #items: array:1 [ …1] #escapeWhenCastingToString: false } "parent_branches" => Illuminate\Database\Eloquent\Collection {#1180 #items: array:2 [ …2] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1217 #items: array:3 [ …3] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "1108095" "type" => "task" ] "previous" => array:2 [ "refs" => "1108093" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1236 #items: array:1 [ …1] #escapeWhenCastingToString: false } "page" => array:2 [ "refs" => "1097855" "type" => "book_page" ] ] #original: array:24 [ "id" => 1108094 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "113" "field_page_end" => null "field_url" => "/9-klass/algebra/kokshetau-soltan-uchebnik/1-370" "field_display_title" => "370" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1172} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1174} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1175} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1180} "content" => Illuminate\Database\Eloquent\Collection {#1217} "next" => array:2 [ "refs" => "1108095" "type" => "task" ] "previous" => array:2 [ "refs" => "1108093" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1236} "page" => array:2 [ "refs" => "1097855" "type" => "book_page" ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 1 => App\Models\Task {#1237 #connection: "mysql" #table: "tasks" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 1108095 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "113" "field_page_end" => null "field_url" => "/9-klass/algebra/kokshetau-soltan-uchebnik/1-371" "field_display_title" => "371" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1238 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1239 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1240 #items: array:1 [ …1] #escapeWhenCastingToString: false } "parent_branches" => Illuminate\Database\Eloquent\Collection {#1241 #items: array:2 [ …2] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1242 #items: array:3 [ …3] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "1108096" "type" => "task" ] "previous" => array:2 [ "refs" => "1108094" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1249 #items: array:1 [ …1] #escapeWhenCastingToString: false } "page" => array:2 [ "refs" => "1097855" "type" => "book_page" ] ] #original: array:24 [ "id" => 1108095 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "113" "field_page_end" => null "field_url" => "/9-klass/algebra/kokshetau-soltan-uchebnik/1-371" "field_display_title" => "371" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1238} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1239} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1240} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1241} "content" => Illuminate\Database\Eloquent\Collection {#1242} "next" => array:2 [ "refs" => "1108096" "type" => "task" ] "previous" => array:2 [ "refs" => "1108094" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1249} "page" => array:2 [ "refs" => "1097855" "type" => "book_page" ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 2 => App\Models\Task {#1250 #connection: "mysql" #table: "tasks" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 1108096 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "113" "field_page_end" => null "field_url" => "/9-klass/algebra/kokshetau-soltan-uchebnik/1-372" "field_display_title" => "372" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1251 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1252 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1253 #items: array:1 [ …1] #escapeWhenCastingToString: false } "parent_branches" => Illuminate\Database\Eloquent\Collection {#1254 #items: array:2 [ …2] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1255 #items: array:3 [ …3] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "1108097" "type" => "task" ] "previous" => array:2 [ "refs" => "1108095" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1262 #items: array:1 [ …1] #escapeWhenCastingToString: false } "page" => array:2 [ "refs" => "1097855" "type" => "book_page" ] ] #original: array:24 [ "id" => 1108096 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "113" "field_page_end" => null "field_url" => "/9-klass/algebra/kokshetau-soltan-uchebnik/1-372" "field_display_title" => "372" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1251} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1252} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1253} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1254} "content" => Illuminate\Database\Eloquent\Collection {#1255} "next" => array:2 [ "refs" => "1108097" "type" => "task" ] "previous" => array:2 [ "refs" => "1108095" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1262} "page" => array:2 [ "refs" => "1097855" "type" => "book_page" ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 3 => App\Models\Task {#1263 #connection: "mysql" #table: "tasks" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 1108097 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "113" "field_page_end" => null "field_url" => "/9-klass/algebra/kokshetau-soltan-uchebnik/1-373" "field_display_title" => "373" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1264 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1265 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1266 #items: array:1 [ …1] #escapeWhenCastingToString: false } "parent_branches" => Illuminate\Database\Eloquent\Collection {#1267 #items: array:2 [ …2] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1268 #items: array:3 [ …3] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "1108098" "type" => "task" ] "previous" => array:2 [ "refs" => "1108096" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1275 #items: array:1 [ …1] #escapeWhenCastingToString: false } "page" => array:2 [ "refs" => "1097855" "type" => "book_page" ] ] #original: array:24 [ "id" => 1108097 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "113" "field_page_end" => null "field_url" => "/9-klass/algebra/kokshetau-soltan-uchebnik/1-373" "field_display_title" => "373" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1264} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1265} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1266} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1267} "content" => Illuminate\Database\Eloquent\Collection {#1268} "next" => array:2 [ "refs" => "1108098" "type" => "task" ] "previous" => array:2 [ "refs" => "1108096" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1275} "page" => array:2 [ "refs" => "1097855" "type" => "book_page" ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 4 => App\Models\Task {#1276 #connection: "mysql" #table: "tasks" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 1108098 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "113" "field_page_end" => null "field_url" => "/9-klass/algebra/kokshetau-soltan-uchebnik/1-374" "field_display_title" => "374" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1277 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1278 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1279 #items: array:1 [ …1] #escapeWhenCastingToString: false } "parent_branches" => Illuminate\Database\Eloquent\Collection {#1280 #items: array:2 [ …2] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1281 #items: array:3 [ …3] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "1108099" "type" => "task" ] "previous" => array:2 [ "refs" => "1108097" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1288 #items: array:1 [ …1] #escapeWhenCastingToString: false } "page" => array:2 [ "refs" => "1097855" "type" => "book_page" ] ] #original: array:24 [ "id" => 1108098 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "113" "field_page_end" => null "field_url" => "/9-klass/algebra/kokshetau-soltan-uchebnik/1-374" "field_display_title" => "374" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1277} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1278} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1279} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1280} "content" => Illuminate\Database\Eloquent\Collection {#1281} "next" => array:2 [ "refs" => "1108099" "type" => "task" ] "previous" => array:2 [ "refs" => "1108097" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1288} "page" => array:2 [ "refs" => "1097855" "type" => "book_page" ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 5 => App\Models\Task {#1289 #connection: "mysql" #table: "tasks" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 1108099 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "113" "field_page_end" => null "field_url" => "/9-klass/algebra/kokshetau-soltan-uchebnik/1-375" "field_display_title" => "375" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1290 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1291 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1292 #items: array:1 [ …1] #escapeWhenCastingToString: false } "parent_branches" => Illuminate\Database\Eloquent\Collection {#1293 #items: array:2 [ …2] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1294 #items: array:3 [ …3] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "1108100" "type" => "task" ] "previous" => array:2 [ "refs" => "1108098" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1301 #items: array:1 [ …1] #escapeWhenCastingToString: false } "page" => array:2 [ "refs" => "1097855" "type" => "book_page" ] ] #original: array:24 [ "id" => 1108099 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "113" "field_page_end" => null "field_url" => "/9-klass/algebra/kokshetau-soltan-uchebnik/1-375" "field_display_title" => "375" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1290} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1291} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1292} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1293} "content" => Illuminate\Database\Eloquent\Collection {#1294} "next" => array:2 [ "refs" => "1108100" "type" => "task" ] "previous" => array:2 [ "refs" => "1108098" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1301} "page" => array:2 [ "refs" => "1097855" "type" => "book_page" ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } ] #original: array:21 [ "id" => 1097855 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "113" "field_url" => "/9-klass/algebra/kokshetau-soltan-uchebnik/page-113" "field_display_title" => "113" "field_folder" => "folder1" "field_image_name" => "113" "field_branch_parent" => Illuminate\Database\Eloquent\Collection {#1131} "field_weight" => "0" "field_book_parent" => Illuminate\Database\Eloquent\Collection {#1130} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "edition_groups" => Illuminate\Database\Eloquent\Collection {#1160} "content" => Illuminate\Database\Eloquent\Collection {#1161} "next" => array:2 [ "refs" => "1097856" "type" => "book_page" ] "previous" => array:2 [ "refs" => "1097854" "type" => "book_page" ] "tasks" => Illuminate\Database\Eloquent\Collection {#1170} ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1108098 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "113" "field_page_end" => null "field_url" => "/9-klass/algebra/kokshetau-soltan-uchebnik/1-374" "field_display_title" => "374" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#331} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1026} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#342} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1061} "content" => Illuminate\Database\Eloquent\Collection {#1098} "next" => array:2 [ "refs" => "1108099" "type" => "task" ] "previous" => array:2 [ "refs" => "1108097" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1123} "page" => array:2 [ "refs" => "1097855" "type" => "book_page" ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] }
№374 (с. 113)
Условие. №374 (с. 113)
скриншот условия
374. Является ли арифметической прогрессией последовательность, график которой изображен на рисунке 37, а, б? Если является, то запишите формулу ее $n$-го члена.
а)
б)
Рисунок 37
Решение. №374 (с. 113)
Решение 2 (rus). №374 (с. 113)
а)
Арифметическая прогрессия — это числовая последовательность, каждый член которой, начиная со второго, равен предыдущему, сложенному с одним и тем же числом, называемым разностью прогрессии (d). Чтобы определить, является ли последовательность на графике арифметической прогрессией, найдем её члены и проверим, постоянна ли разность между ними.
По графику на рисунке 37, а) определим первые несколько членов последовательности $a_n$, где n — номер члена (ось x), а $a_n$ — его значение (ось y):
$a_1 = 7$
$a_2 = 5,5$
$a_3 = 4$
$a_4 = 2,5$
$a_5 = 1$
Теперь найдем разность d между соседними членами:
$d_1 = a_2 - a_1 = 5,5 - 7 = -1,5$
$d_2 = a_3 - a_2 = 4 - 5,5 = -1,5$
$d_3 = a_4 - a_3 = 2,5 - 4 = -1,5$
$d_4 = a_5 - a_4 = 1 - 2,5 = -1,5$
Так как разность между всеми последовательными членами постоянна и равна -1,5, данная последовательность является арифметической прогрессией. Первый член прогрессии $a_1 = 7$, а её разность $d = -1,5$.
Запишем формулу n-го члена арифметической прогрессии: $a_n = a_1 + (n-1)d$.
Подставим найденные значения $a_1$ и d:
$a_n = 7 + (n-1) \cdot (-1,5)$
Упростим выражение:
$a_n = 7 - 1,5n + 1,5$
$a_n = 8,5 - 1,5n$
Ответ: Да, является. Формула n-го члена: $a_n = 8,5 - 1,5n$.
б)
Аналогично проанализируем график на рисунке 37, б). Определим первые несколько членов последовательности:
$a_1 = 6$
$a_2 = 4$
$a_3 = 4$
$a_4 = 2$
$a_5 = 2$
Теперь найдем разность между соседними членами:
$d_1 = a_2 - a_1 = 4 - 6 = -2$
$d_2 = a_3 - a_2 = 4 - 4 = 0$
Разности между соседними членами не равны ($-2 \neq 0$). Следовательно, эта последовательность не является арифметической прогрессией, так как у неё нет постоянной разности.
Ответ: Нет, не является.
Другие задания:
Помогло решение? Оставьте отзыв в комментариях ниже.
Присоединяйтесь к Телеграм-группе @top_gdz
ПрисоединитьсяМы подготовили для вас ответ c подробным объяснением домашего задания по алгебре за 9 класс, для упражнения номер 374 расположенного на странице 113 к учебнику 2019 года издания для учащихся школ и гимназий.
Теперь на нашем сайте ГДЗ.ТОП вы всегда легко и бесплатно найдёте условие с правильным ответом на вопрос «Как решить ДЗ» и «Как сделать» задание по алгебре к упражнению №374 (с. 113), авторов: Солтан (Генадий Николаевич), Солтан (Алла Евгеньевна), Жумадилова (Аманбала Жумадиловна), учебного пособия издательства Кокшетау.