{"id":1433,"date":"2025-12-31T08:26:07","date_gmt":"2025-12-31T07:26:07","guid":{"rendered":"http:\/\/mymatma.pl\/?p=1433"},"modified":"2025-12-31T08:27:41","modified_gmt":"2025-12-31T07:27:41","slug":"zadanie-145","status":"publish","type":"post","link":"https:\/\/mymatma.pl\/?p=1433","title":{"rendered":"Zadanie 145"},"content":{"rendered":"\n<p><strong>zadanie 11 \u2013 maj 2018 (1pkt)<\/strong><\/p>\n\n\n\n<p>Dany jest ci\u0105g (a<sub>n<\/sub>) okre\u015blony wzorem a<sub>n<\/sub>=(5\u22122n)\/6 dla n\u22651 . Ci\u0105g ten jest:<\/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<p>a) arytmetyczny i jego r\u00f3\u017cnica jest r\u00f3wna r=\u2212(1\/3)<\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<p>b) arytmetyczny i jego r\u00f3\u017cnica jest r\u00f3wna r=\u22122<\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<p>c) geometryczny i jego iloraz jest r\u00f3wny q=\u2212(1\/3)<\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<p>d) geometryczny i jego iloraz jest r\u00f3wny q=5\/6<\/p>\n<\/div>\n<\/div>\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_69e22b4b61d8c\">\n        <button class=\"premium-btn-odp\"\n                data-id=\"odp_69e22b4b61d8c\"\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 ten jest: a) arytmetyczny i jego r\u00f3\u017cnica jest r\u00f3wna r = \u2212(1\/3)<\/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_69e22b4b61d98\">\n        <button class=\"premium-btn-wyjasnienie\"\n                data-id=\"wyjasnienie_69e22b4b61d98\"\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:<\/p>\n<p><code>a\u2099 = (5 \u2212 2n) \/ 6<\/code><\/p>\n\n<h3>Krok 1: Sprawdzenie, czy ci\u0105g jest arytmetyczny<\/h3>\n\n<p>Obliczamy r\u00f3\u017cnic\u0119 mi\u0119dzy kolejnymi wyrazami:<\/p>\n\n<p>\na\u2099\u208a\u2081 = (5 \u2212 2(n+1)) \/ 6 = (5 \u2212 2n \u2212 2) \/ 6 = (3 \u2212 2n) \/ 6\n<\/p>\n\n<p>R\u00f3\u017cnica ci\u0105gu:<\/p>\n\n<p>\na\u2099\u208a\u2081 \u2212 a\u2099 = [(3 \u2212 2n)\/6] \u2212 [(5 \u2212 2n)\/6]\n<\/p>\n\n<p>Odejmujemy liczniki:<\/p>\n\n<p>\n= (3 \u2212 2n \u2212 5 + 2n) \/ 6 = (\u22122) \/ 6 = \u22121\/3\n<\/p>\n\n<h3>Wniosek<\/h3>\n\n<p>R\u00f3\u017cnica mi\u0119dzy kolejnymi wyrazami jest sta\u0142a i wynosi <strong>\u22121\/3<\/strong>, wi\u0119c ci\u0105g jest arytmetyczny.<\/p>\n\n<p><strong>Prawid\u0142owa odpowied\u017a: a)<\/strong><\/p>\n\n        <\/div>\n    <\/div>\n    \n<\/div>\n<\/div>\n\n\n\n<p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>zadanie 11 \u2013 maj 2018 (1pkt) Dany jest ci\u0105g (an) okre\u015blony wzorem an=(5\u22122n)\/6 dla n\u22651 . Ci\u0105g ten jest: a) arytmetyczny i jego r\u00f3\u017cnica jest r\u00f3wna r=\u2212(1\/3) b) arytmetyczny i jego r\u00f3\u017cnica jest r\u00f3wna r=\u22122 c) geometryczny i jego iloraz jest r\u00f3wny q=\u2212(1\/3) d) geometryczny i jego iloraz jest r\u00f3wny q=5\/6<\/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":[25,96,204,81,83],"tags":[23,95,205],"class_list":["post-1433","post","type-post","status-publish","format-standard","hentry","category-ciag-arytmetyczny","category-maj-2018","category-rozne","category-zadania-maturalne","category-zadania-tematami","tag-ciag-arytmetyczny","tag-maj-2018","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 11 \u2013 maj 2018 (1pkt) Dany jest ci\u0105g (an) okre\u015blony wzorem an=(5\u22122n)\/6 dla n\u22651 . Ci\u0105g ten jest: a) arytmetyczny i jego r\u00f3\u017cnica jest r\u00f3wna r=\u2212(1\/3) b) arytmetyczny i jego r\u00f3\u017cnica jest r\u00f3wna r=\u22122 c) geometryczny i jego iloraz jest r\u00f3wny q=\u2212(1\/3) d) geometryczny i jego iloraz jest r\u00f3wny q=5\/6","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/mymatma.pl\/index.php?rest_route=\/wp\/v2\/posts\/1433","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=1433"}],"version-history":[{"count":3,"href":"https:\/\/mymatma.pl\/index.php?rest_route=\/wp\/v2\/posts\/1433\/revisions"}],"predecessor-version":[{"id":1439,"href":"https:\/\/mymatma.pl\/index.php?rest_route=\/wp\/v2\/posts\/1433\/revisions\/1439"}],"wp:attachment":[{"href":"https:\/\/mymatma.pl\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1433"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mymatma.pl\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1433"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mymatma.pl\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1433"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}