{"id":1475,"date":"2025-12-31T09:23:24","date_gmt":"2025-12-31T08:23:24","guid":{"rendered":"http:\/\/mymatma.pl\/?p=1475"},"modified":"2025-12-31T09:29:29","modified_gmt":"2025-12-31T08:29:29","slug":"zadanie-150","status":"publish","type":"post","link":"https:\/\/mymatma.pl\/?p=1475","title":{"rendered":"Zadanie 150"},"content":{"rendered":"\n<p><strong>zadanie 24 \u2013 informator CKE (zadanie otwarte) (2 pkt)<\/strong><\/p>\n\n\n\n<p>Dany jest ci\u0105g (a<sub>n<\/sub>) okre\u015blony wzorem og\u00f3lnym: a<sub>n<\/sub>=4n\u22129 dla ka\u017cdej liczby naturalnej n\u22651. Wyka\u017c, \u017ce ci\u0105g (a<sub>n<\/sub>) jest arytmetyczny.<\/p>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-28f84493 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n    <div class=\"premium-wrapper-odp\" id=\"odp_69e22b8f02efc\">\n        <button class=\"premium-btn-odp\"\n                data-id=\"odp_69e22b8f02efc\"\n                style=\"margin-top:10px; padding:12px 20px; background:#28a745; color:#fff; border-radius:25px; border:none; cursor:pointer; font-weight:bold;\">\n            Poka\u017c odpowied\u017a\n        <\/button>\n\n        <div class=\"premium-content-odp\" style=\"display:none; padding:15px; border:1px solid #28a745; margin-top:10px; background:#e6ffe6; border-radius:25px;\">\n            \nCi\u0105g jest arytmetyczny, poniewa\u017c jego r\u00f3\u017cnica jest sta\u0142a i wynosi <strong>4<\/strong>.<\/p>.\n        <\/div>\n    <\/div>\n    \n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n    <div class=\"premium-wrapper-wyjasnienie\" id=\"wyjasnienie_69e22b8f02f07\">\n        <button class=\"premium-btn-wyjasnienie\"\n                data-id=\"wyjasnienie_69e22b8f02f07\"\n                style=\"margin-top:10px; padding:12px 20px; background:#28a745; color:#fff; border-radius:25px; border:none; cursor:pointer; font-weight:bold;\">\n            Poka\u017c wyja\u015bnienie\n        <\/button>\n\n        <div class=\"premium-content-wyjasnienie\" style=\"display:none; padding:15px; border:1px solid #28a745; margin-top:10px; background:#e6ffe6; border-radius:25px;\">\n            \n<h2>Wyja\u015bnienie<\/h2>\n\n<p>Ci\u0105g jest okre\u015blony wzorem og\u00f3lnym:<\/p>\n\n<p><code>a\u2099 = 4n \u2212 9<\/code><\/p>\n\n<h3>Krok 1: Sprawdzenie r\u00f3\u017cnicy ci\u0105gu<\/h3>\n\n<p>W ci\u0105gu arytmetycznym r\u00f3\u017cnica <code>r<\/code> jest sta\u0142a i wynosi:<\/p>\n\n<p><code>r = a\u2099\u208a\u2081 \u2212 a\u2099<\/code><\/p>\n\n<h3>Krok 2: Obliczenie r\u00f3\u017cnicy<\/h3>\n\n<p>\na\u2099\u208a\u2081 = 4(n+1) \u2212 9 = 4n + 4 \u2212 9 = 4n \u2212 5<br>\na\u2099 = 4n \u2212 9\n<\/p>\n\n<p>R\u00f3\u017cnica:<\/p>\n\n<p>\na\u2099\u208a\u2081 \u2212 a\u2099 = (4n \u2212 5) \u2212 (4n \u2212 9) = 4\n<\/p>\n\n<h3>Wniosek<\/h3>\n\n<p>R\u00f3\u017cnica mi\u0119dzy kolejnymi wyrazami jest sta\u0142a i r\u00f3wna <strong>4<\/strong>, wi\u0119c ci\u0105g jest arytmetyczny.<\/p>\n\n        <\/div>\n    <\/div>\n    \n<\/div>\n<\/div>\n\n\n\n<p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>zadanie 24 \u2013 informator CKE (zadanie otwarte) (2 pkt) Dany jest ci\u0105g (an) okre\u015blony wzorem og\u00f3lnym: an=4n\u22129 dla ka\u017cdej liczby naturalnej n\u22651. Wyka\u017c, \u017ce ci\u0105g (an) jest arytmetyczny.<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"saved_in_kubio":false,"_uag_custom_page_level_css":"","_themeisle_gutenberg_block_has_review":false,"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[25,130,204,81,83],"tags":[23,129,205],"class_list":["post-1475","post","type-post","status-publish","format-standard","hentry","category-ciag-arytmetyczny","category-informator-cke","category-rozne","category-zadania-maturalne","category-zadania-tematami","tag-ciag-arytmetyczny","tag-informator-cke","tag-rozne"],"jetpack_featured_media_url":"","uagb_featured_image_src":{"full":false,"thumbnail":false,"medium":false,"medium_large":false,"large":false,"1536x1536":false,"2048x2048":false,"kubio-fullhd":false,"woocommerce_thumbnail":false,"woocommerce_single":false,"woocommerce_gallery_thumbnail":false},"uagb_author_info":{"display_name":"adminmymatma","author_link":"https:\/\/mymatma.pl\/?author=1"},"uagb_comment_info":0,"uagb_excerpt":"zadanie 24 \u2013 informator CKE (zadanie otwarte) (2 pkt) Dany jest ci\u0105g (an) okre\u015blony wzorem og\u00f3lnym: an=4n\u22129 dla ka\u017cdej liczby naturalnej n\u22651. Wyka\u017c, \u017ce ci\u0105g (an) jest arytmetyczny.","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/mymatma.pl\/index.php?rest_route=\/wp\/v2\/posts\/1475","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/mymatma.pl\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mymatma.pl\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mymatma.pl\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/mymatma.pl\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=1475"}],"version-history":[{"count":2,"href":"https:\/\/mymatma.pl\/index.php?rest_route=\/wp\/v2\/posts\/1475\/revisions"}],"predecessor-version":[{"id":1477,"href":"https:\/\/mymatma.pl\/index.php?rest_route=\/wp\/v2\/posts\/1475\/revisions\/1477"}],"wp:attachment":[{"href":"https:\/\/mymatma.pl\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1475"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mymatma.pl\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1475"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mymatma.pl\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1475"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}