{"243r0":{"state":{"logoProps":{"url":"https://yandex.kz"},"formProps":{"action":"https://yandex.kz/search","searchLabel":"Найти"},"services":{"items":[]},"userProps":{"loggedIn":false,"ariaLabel":"Меню","plus":false,"birthdayHat":false,"child":false,"dialogProps":{"host":"yandex.kz","lang":"ru","project":"neurolib","queryParams":{"exp_flags":"skin","preset":"oceania","utm_source":"portal-neurolib"},"retpath":"https%3A%2F%2Fyandex.kz%2Fyanswers%2Fc%2Fgylym-jane-bilim%2Fq%2Farifmetikalyk-progrecciyanyn-formulacy-kanday-2332840323%3Fncrnd%3D61957","tld":"kz","platform":"desktop"},"className":"PortalHeader-User"},"suggestProps":{"selectors":{"form":".HeaderForm","input":".HeaderForm-Input","submit":".HeaderForm-Submit","clear":".HeaderForm-Clear","layout":".HeaderForm-InputWrapper"},"suggestUrl":"https://yandex.com.tr/suggest/suggest-ya.cgi?show_experiment=222&show_experiment=224","deleteUrl":"https://yandex.com.tr/suggest-delete-text?srv=web&text_to_delete=","suggestPlaceholder":"Поиск с Нейро","platform":"desktop","hideKeyboardOnScroll":false,"additionalFormClasses":["mini-suggest_theme_tile","mini-suggest_overlay_tile","mini-suggest_expanding_yes","mini-suggest_prevent-empty_yes","mini-suggest_type-icon_yes","mini-suggest_personal_yes","mini-suggest_type-icon_yes","mini-suggest_rich_yes","mini-suggest_overlay_dark","mini-suggest_large_yes","mini-suggest_copy-fact_yes","mini-suggest_clipboard_yes","mini-suggest_turboapp_yes","mini-suggest_expanding_yes","mini-suggest_affix_yes","mini-suggest_carousel_yes","mini-suggest_traffic_yes","mini-suggest_re-request_yes","mini-suggest_source_yes","mini-suggest_favicon_yes","mini-suggest_more","mini-suggest_long-fact_yes","mini-suggest_hide-keyboard_yes","mini-suggest_clear-on-submit_yes","mini-suggest_focus-on-change_yes","mini-suggest_short-fact_yes","mini-suggest_app_yes","mini-suggest_grouping_yes","mini-suggest_entity-suggest_yes","mini-suggest_redesigned-navs_yes","mini-suggest_title-multiline_yes","mini-suggest_type-icon-wrapped_yes","mini-suggest_fulltext-highlight_yes","mini-suggest_fulltext-insert_yes","mini-suggest_lines_multi"],"counter":{"service":"neurolib_com_tr_desktop","url":"//yandex.ru/clck/jclck","timeout":300,"params":{"dtype":"stred","pid":"0","cid":"2873"}},"noSubmit":false,"formAction":"https://yandex.kz/search","tld":"kz","suggestParams":{},"disableWebSuggest":false},"context":{"query":"","reqid":"1771453208316293-8169047858285528804-balancer-l7leveler-kubr-yp-klg-180-BAL","lr":"20815","aliceDeeplink":"{\"text\":\"\"}"},"baobab":{"parentNode":{"context":{"genInfo":{"prefix":"243rw01-0-1"},"ui":"desktop","service":"neurolib","fast":{"name":"neuro_library","subtype":"header"}}}}},"type":"neuro_library","subtype":"header"},"243r1":{"state":{"links":[{"id":"main","url":"/yanswers/","title":"Главная","target":"_self"},{"id":"technologies","url":"/yanswers/c/tehnologiyalar","title":"Технологии","target":"_self"},{"id":"psychology-and-relationships","url":"/yanswers/c/psihologiya-jane-qarim-qatinas","title":"Психология и отношения","target":"_self"},{"id":"science-and-education","url":"/yanswers/c/gylym-jane-bilim","title":"Наука и образование","target":"_self"},{"id":"food","url":"/yanswers/c/tamaq-jane-as-onimderi","title":"Еда","target":"_self"},{"id":"culture-and-art","url":"/yanswers/c/madeniet-pen-oner","title":"Культура и искусство","target":"_self"},{"id":"tv-and-films","url":"/yanswers/c/tv-jane-filmder","title":"Фильмы и сериалы","target":"_self"},{"id":"economics-and-finance","url":"/yanswers/c/ekonomika-jane-qarjy","title":"Экономика и финансы","target":"_self"},{"id":"games","url":"/yanswers/c/oyindar","title":"Игры","target":"_self"},{"id":"sport","url":"/yanswers/c/sport","title":"Спорт","target":"_self"},{"id":"beauty-and-style","url":"/yanswers/c/sululiq-pen-stil","title":"Красота и мода","target":"_self"},{"id":"useful-tips","url":"/yanswers/c/paydaly-kenester","title":"Полезные советы","target":"_self"},{"id":"auto","url":"/yanswers/c/avto","title":"Авто","target":"_self"},{"id":"law","url":"/yanswers/c/zan","title":"Право","target":"_self"},{"id":"travel","url":"/yanswers/c/sayahat","title":"Путешествия","target":"_self"},{"id":"animals-and-nature","url":"/yanswers/c/januarlar-men-tabigat","title":"Животные и природа","target":"_self"},{"id":"health","url":"/yanswers/c/densaulyq","title":"Здоровье","target":"_self"},{"id":"other","url":"/yanswers/c/basqasy","title":"Другое","target":"_self"}],"activeLinkId":"science-and-education","title":"Категории","baobab":{"parentNode":{"context":{"genInfo":{"prefix":"243rw02-0-1"},"ui":"desktop","service":"neurolib","fast":{"name":"neuro_library","subtype":"header-categories"}}}}},"type":"neuro_library","subtype":"header-categories"},"243r2":{"state":{"tld":"kz","markdown":"Арифметикалық прогрессияның формуласы:\n\n* **n-ші членінің формуласы** [```1```](https://www.youtube.com/watch?v=vXOEfy4cKmo)[```2```](https://tr-page.yandex.ru/translate?lang=ru-kk&url=https%3A%2F%2Fru.wikipedia.org%2Fwiki%2F%25D0%2590%25D1%2580%25D0%25B8%25D1%2584%25D0%25BC%25D0%25B5%25D1%2582%25D0%25B8%25D0%25BA%25D0%25BE-%25D0%25B3%25D0%25B5%25D0%25BE%25D0%25BC%25D0%25B5%25D1%2582%25D1%2580%25D0%25B8%25D1%2587%25D0%25B5%25D1%2581%25D0%25BA%25D0%25B0%25D1%258F_%25D0%25BF%25D1%2580%25D0%25BE%25D0%25B3%25D1%2580%25D0%25B5%25D1%2581%25D1%2581%25D0%25B8%25D1%258F)[```3```](https://infourok.ru/ashy%D2%9B-saba%D2%9B-zhospary-arifmetikaly%D2%9B-zh%D3%99ne-geometriyaly%D2%9B-progressiya-4458263.html): an = a1 + (n - 1)d,\n\n* *мұнда:*\n\n * a1 — прогрессияның бірінші члені [```1```](https://www.youtube.com/watch?v=vXOEfy4cKmo);\n * d — араласу [```1```](https://www.youtube.com/watch?v=vXOEfy4cKmo)[```3```](https://infourok.ru/ashy%D2%9B-saba%D2%9B-zhospary-arifmetikaly%D2%9B-zh%D3%99ne-geometriyaly%D2%9B-progressiya-4458263.html);\n * n — членнің нөмірі [```1```](https://www.youtube.com/watch?v=vXOEfy4cKmo).\n\n*Арифметикалық прогрессиясөздердің бірінше нөмірлерінің қосындысы (аn) ашқылдырады [```1```](https://www.youtube.com/watch?v=vXOEfy4cKmo): Sn = n/2 * (a1 + an) [```1```](https://www.youtube.com/watch?v=vXOEfy4cKmo).*","sources":[{"sourceId":1,"url":"https://www.youtube.com/watch?v=vXOEfy4cKmo","title":"Арифметическая и геометрическая прогрессия - YouTube","shownUrl":"https://www.youtube.com/watch?v=vXOEfy4cKmo","rel":"nofollow"},{"sourceId":2,"url":"https://tr-page.yandex.ru/translate?lang=ru-kk&url=https%3A%2F%2Fru.wikipedia.org%2Fwiki%2F%25D0%2590%25D1%2580%25D0%25B8%25D1%2584%25D0%25BC%25D0%25B5%25D1%2582%25D0%25B8%25D0%25BA%25D0%25BE-%25D0%25B3%25D0%25B5%25D0%25BE%25D0%25BC%25D0%25B5%25D1%2582%25D1%2580%25D0%25B8%25D1%2587%25D0%25B5%25D1%2581%25D0%25BA%25D0%25B0%25D1%258F_%25D0%25BF%25D1%2580%25D0%25BE%25D0%25B3%25D1%2580%25D0%25B5%25D1%2581%25D1%2581%25D0%25B8%25D1%258F","title":"Арифметикалық-геометриялық прогрессия — Википедия","shownUrl":"https://tr-page.yandex.ru/translate?lang=ru-kk&url=https%3A%2F%2Fru.wikipedia.org%2Fwiki%2F%25D0%2590%25D1%2580%25D0%25B8%25D1%2584%25D0%25BC%25D0%25B5%25D1%2582%25D0%25B8%25D0%25BA%25D0%25BE-%25D0%25B3%25D0%25B5%25D0%25BE%25D0%25BC%25D0%25B5%25D1%2582%25D1%2580%25D0%25B8%25D1%2587%25D0%25B5%25D1%2581%25D0%25BA%25D0%25B0%25D1%258F_%25D0%25BF%25D1%2580%25D0%25BE%25D0%25B3%25D1%2580%25D0%25B5%25D1%2581%25D1%2581%25D0%25B8%25D1%258F","rel":"nofollow"},{"sourceId":3,"url":"https://infourok.ru/ashy%D2%9B-saba%D2%9B-zhospary-arifmetikaly%D2%9B-zh%D3%99ne-geometriyaly%D2%9B-progressiya-4458263.html","title":"Ашық сабақ жоспары Арифметикалық және... | Инфоурок","shownUrl":"https://infourok.ru/ashy%D2%9B-saba%D2%9B-zhospary-arifmetikaly%D2%9B-zh%D3%99ne-geometriyaly%D2%9B-progressiya-4458263.html","rel":"nofollow"},{"sourceId":4,"url":"https://www.yaklass.ru/p/osnovnoj-gosudarstvennyj-ekzamen/matematika/oge-trenazher-7304039/zadachi-na-arifmeticheskuiu-i-geometricheskuiu-progressii-zadanie-14-7327746/re-adcc6f8d-ea50-4977-a30c-83bfba6bf764","title":"Арифметическая и геометрическая прогрессии — урок.","shownUrl":"https://www.yaklass.ru/p/osnovnoj-gosudarstvennyj-ekzamen/matematika/oge-trenazher-7304039/zadachi-na-arifmeticheskuiu-i-geometricheskuiu-progressii-zadanie-14-7327746/re-adcc6f8d-ea50-4977-a30c-83bfba6bf764","rel":"nofollow"},{"sourceId":5,"url":"https://kopilkaurokov.ru/algebra/planirovanie/arifmietikalyk_zh_nie_ghieomietriialyk_proghriessiialar","title":"Арифметикалық және геометриялық прогрессиялар...","shownUrl":"https://kopilkaurokov.ru/algebra/planirovanie/arifmietikalyk_zh_nie_ghieomietriialyk_proghriessiialar","rel":"nofollow"},{"sourceId":6,"url":"https://ziatker.kz/docx/asyq_sabaq_arifmetikalyq_jane_geometriyalyq_progressiyalar_9_synyp_9605.html","title":"Ашық сабақ \"Арифметикалық және геометриялық...\"","shownUrl":"https://ziatker.kz/docx/asyq_sabaq_arifmetikalyq_jane_geometriyalyq_progressiyalar_9_synyp_9605.html","rel":"nofollow"},{"sourceId":7,"url":"https://stud.kz/referat/show/109221","title":"Арифметикалық және геометриялық прогрессиялар","shownUrl":"https://stud.kz/referat/show/109221","rel":"nofollow"},{"sourceId":8,"url":"https://multiurok.ru/files/arifmetikalyk-zh-ne-geometriialyk-progressiialar.html","title":"Арифметикалық және геометриялық прогрессиялар","shownUrl":"https://multiurok.ru/files/arifmetikalyk-zh-ne-geometriialyk-progressiialar.html","rel":"nofollow"},{"sourceId":9,"url":"https://ust.kz/word/arifmetikalyq_jane_geometriyalyq_progressiya-101060.html","title":"Арифметикалық және геометриялық прогрессия","shownUrl":"https://ust.kz/word/arifmetikalyq_jane_geometriyalyq_progressiya-101060.html","rel":"nofollow"},{"sourceId":10,"url":"https://bilimland.ru/kk/plans/4039","title":"Арифметикалық және геометриялық прогрессиялар...","shownUrl":"https://bilimland.ru/kk/plans/4039","rel":"nofollow"}],"isHermione":false,"headerProps":{"header":"Арифметикалық прогрессияның формуласы қандай?","homeUrl":"/yanswers/","categoryUrl":"/yanswers/c/gylym-jane-bilim","categoryTitle":"Наука и образование","share":true,"canUseNativeShare":false,"hideYazekaHeader":false,"tags":[],"extralinksItems":[{"variant":"reportFeedback","reportFeedback":{"feature":"YazekaAnswers","title":"Что не так в этом ответе?","checkBoxLabels":[{"value":"Неприемлемый или оскорбительный ответ"},{"value":"Нет ответа на мой вопрос"},{"value":"Есть фактические ошибки"},{"value":"Мало информации"},{"value":"Информация устарела"},{"value":"Ошибки отображения"},{"value":"Нет доверия источникам ответа"},{"value":"Не нужен ответ по этому вопросу"},{"value":"Другое"}]}}]},"suggestProps":{"suggestItems":[{"id":-1,"url":"/search?text=%D0%90%D1%80%D0%B8%D1%84%D0%BC%D0%B5%D1%82%D0%B8%D0%BA%D0%B0%D0%BB%D1%8B%D2%9B+%D0%BF%D1%80%D0%BE%D0%B3%D1%80%D0%B5%D1%81%D1%81%D0%B8%D1%8F%D0%BD%D1%8B%D2%A3+%D1%84%D0%BE%D1%80%D0%BC%D1%83%D0%BB%D0%B0%D1%81%D1%8B+%D2%9B%D0%B0%D0%BD%D0%B4%D0%B0%D0%B9%3F&promo=force_neuro","text":"Получите больше информации"}]},"feedbackProps":{"feature":"YazekaAnswers","baseProps":{"metaFields":{"yandexuid":"4791631611771453206","reqid":"1771453208316293-8169047858285528804-balancer-l7leveler-kubr-yp-klg-180-BAL"}},"positiveCheckboxLabels":[{"value":"Очень понравился ответ"},{"value":"В ответе есть нужная информация"},{"value":"Хорошая структура"},{"value":"Другое"}],"negativeCheckboxLabels":[{"value":"Неприемлемый или оскорбительный ответ"},{"value":"Нет ответа на мой вопрос"},{"value":"Есть фактические ошибки"},{"value":"Мало информации"},{"value":"Информация устарела"},{"value":"Ошибки отображения"},{"value":"Нет доверия источникам ответа"},{"value":"Не нужен ответ по этому вопросу"},{"value":"Другое"}]},"dialogStoreProps":{"baseUrl":""},"globalStoreProps":{"imageBackendUrl":"https://yandex.kz/images-apphost/image-download?cbird=171","query":"","retina":false,"avatarId":"0","isMacOS":false,"brand":"neuro","device":{"isIOS":false,"platform":"desktop"}},"baobab":{"parentNode":{"context":{"genInfo":{"prefix":"243rw03-0-1"},"ui":"desktop","service":"neurolib","fast":{"name":"neuro_library","subtype":"question"}}}}},"type":"neuro_library","subtype":"question"},"243r3":{"state":{"relatedMaterials":[],"baobab":{"parentNode":{"context":{"genInfo":{"prefix":"243rw04-0-1"},"ui":"desktop","service":"neurolib","fast":{"name":"neuro_library","subtype":"related"}}}}},"type":"neuro_library","subtype":"related"},"243r4":{"state":{"tld":"kz","isIos":false,"isQuestionPage":true,"baobab":{"parentNode":{"context":{"genInfo":{"prefix":"243rw05-0-1"},"ui":"desktop","service":"neurolib","fast":{"name":"neuro_library","subtype":"ask_question"}}}}},"type":"neuro_library","subtype":"ask_question"},"243r5":{"state":{"generalLinks":[{"id":"privacy-policy","text":"Политика конфиденциальности","url":"https://yandex.kz/legal/confidential/"},{"id":"terms-of-service","text":"Пользовательское соглашение","url":"https://yandex.kz/legal/neurum_termsofuse/"},{"id":"report-error","text":"Сообщить об ошибке","url":"https://forms.yandex.kz/surveys/13764639.7eee0a3742f85d3f2330de0b5792096e6be7f464/"},{"id":"about-company","text":"О компании","url":"https://company.yandex.ru/"}],"copyright":{"url":"https://yandex.kz","currentYear":2026},"socialLinks":[],"disclaimer":"Ответы сформированы Нейро на основе общедоступной информации. В них могут быть неточности","baobab":{"parentNode":{"context":{"genInfo":{"prefix":"243rw06-0-1"},"ui":"desktop","service":"neurolib","fast":{"name":"neuro_library","subtype":"footer"}}}}},"type":"neuro_library","subtype":"footer"}}