{"id":1323,"date":"2025-12-22T14:37:39","date_gmt":"2025-12-22T13:37:39","guid":{"rendered":"http:\/\/mymatma.pl\/?p=1323"},"modified":"2025-12-22T14:37:43","modified_gmt":"2025-12-22T13:37:43","slug":"zadanie-131","status":"publish","type":"post","link":"https:\/\/mymatma.pl\/?p=1323","title":{"rendered":"Zadanie 131"},"content":{"rendered":"\n<p><strong>zadanie 11 \u2013 maj 2014 (1pkt)<\/strong><\/p>\n\n\n\n<p>Liczby 2,\u22121,\u22124 s\u0105 trzema pocz\u0105tkowymi wyrazami ci\u0105gu arytmetycznego (a<sub>n<\/sub>) , okre\u015blonego dla liczb naturalnych n\u22651 . Wz\u00f3r og\u00f3lny tego ci\u0105gu ma posta\u0107:<\/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) a<sub>n<\/sub>=\u22123n+5<\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<p>b) a<sub>n<\/sub>=n\u22123<\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<p>c) a<sub>n<\/sub>=\u2212n+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) a<sub>n<\/sub>=3n\u22125<\/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_69e22d91e3f6f\">\n        <button class=\"premium-btn-odp\"\n                data-id=\"odp_69e22d91e3f6f\"\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            \nPrawid\u0142owa odpowied\u017a to a) a\u2099 = \u22123n + 5.\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_69e22d91e3f7a\">\n        <button class=\"premium-btn-wyjasnienie\"\n                data-id=\"wyjasnienie_69e22d91e3f7a\"\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<h3>Wyja\u015bnienie<\/h3>\n\n<p>W zadaniu podano trzy kolejne wyrazy ci\u0105gu arytmetycznego:<\/p>\n\n<p style=\"text-align:center;\">\n2, &nbsp; \u22121, &nbsp; \u22124\n<\/p>\n\n<p>Aby sprawdzi\u0107 wz\u00f3r og\u00f3lny, najpierw obliczamy r\u00f3\u017cnic\u0119 ci\u0105gu:<\/p>\n\n<h4>1. Obliczamy r\u00f3\u017cnic\u0119 r<\/h4>\n\n<p style=\"text-align:center;\">\nr = a\u2082 \u2212 a\u2081 = \u22121 \u2212 2 = \u22123\n<\/p>\n\n<p>Sprawdzamy dla kolejnych wyraz\u00f3w:<\/p>\n\n<p style=\"text-align:center;\">\na\u2083 \u2212 a\u2082 = \u22124 \u2212 (\u22121) = \u22123\n<\/p>\n\n<p>R\u00f3\u017cnica jest sta\u0142a, wi\u0119c r = \u22123.<\/p>\n\n<hr>\n\n<h4>2. Korzystamy ze wzoru na n\u2011ty wyraz ci\u0105gu arytmetycznego<\/h4>\n\n<p style=\"text-align:center;\">\na\u2099 = a\u2081 + (n \u2212 1)r\n<\/p>\n\n<p>Podstawiamy dane warto\u015bci:<\/p>\n\n<p style=\"text-align:center;\">\na\u2099 = 2 + (n \u2212 1)(\u22123)\n<\/p>\n\n<p>Upraszczenie:<\/p>\n\n<p style=\"text-align:center;\">\na\u2099 = 2 \u2212 3n + 3\n<\/p>\n\n<p style=\"text-align:center;\">\na\u2099 = \u22123n + 5\n<\/p>\n\n<h3>Odpowied\u017a:<\/h3>\n<p>Wz\u00f3r og\u00f3lny ci\u0105gu to <strong>a\u2099 = \u22123n + 5<\/strong>.<\/p>\n\n        <\/div>\n    <\/div>\n    \n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>zadanie 11 \u2013 maj 2014 (1pkt) Liczby 2,\u22121,\u22124 s\u0105 trzema pocz\u0105tkowymi wyrazami ci\u0105gu arytmetycznego (an) , okre\u015blonego dla liczb naturalnych n\u22651 . Wz\u00f3r og\u00f3lny tego ci\u0105gu ma posta\u0107: a) an=\u22123n+5 b) an=n\u22123 c) an=\u2212n+3 d) an=3n\u22125<\/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":[25,124,203,81,83],"tags":[23,123,202],"class_list":["post-1323","post","type-post","status-publish","format-standard","hentry","category-ciag-arytmetyczny","category-maj-2014","category-wyznaczanie-wzoru-ogolnego","category-zadania-maturalne","category-zadania-tematami","tag-ciag-arytmetyczny","tag-maj-2014","tag-wyznaczanie-wzoru-ogolnego"],"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 2014 (1pkt) Liczby 2,\u22121,\u22124 s\u0105 trzema pocz\u0105tkowymi wyrazami ci\u0105gu arytmetycznego (an) , okre\u015blonego dla liczb naturalnych n\u22651 . Wz\u00f3r og\u00f3lny tego ci\u0105gu ma posta\u0107: a) an=\u22123n+5 b) an=n\u22123 c) an=\u2212n+3 d) an=3n\u22125","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/mymatma.pl\/index.php?rest_route=\/wp\/v2\/posts\/1323","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=1323"}],"version-history":[{"count":1,"href":"https:\/\/mymatma.pl\/index.php?rest_route=\/wp\/v2\/posts\/1323\/revisions"}],"predecessor-version":[{"id":1324,"href":"https:\/\/mymatma.pl\/index.php?rest_route=\/wp\/v2\/posts\/1323\/revisions\/1324"}],"wp:attachment":[{"href":"https:\/\/mymatma.pl\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1323"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mymatma.pl\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1323"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mymatma.pl\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1323"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}