{"id":1472,"date":"2025-12-31T09:07:04","date_gmt":"2025-12-31T08:07:04","guid":{"rendered":"http:\/\/mymatma.pl\/?p=1472"},"modified":"2025-12-31T09:07:49","modified_gmt":"2025-12-31T08:07:49","slug":"zadanie-149","status":"publish","type":"post","link":"https:\/\/mymatma.pl\/?p=1472","title":{"rendered":"Zadanie 149"},"content":{"rendered":"\n<p><strong>zadanie 11 \u2013 sierpie\u0144 2016 (1 pkt)<\/strong><\/p>\n\n\n\n<p>Dla ka\u017cdej liczby ca\u0142kowitej dodatniej n suma n pocz\u0105tkowych wyraz\u00f3w ci\u0105gu arytmetycznego (a<sub>n<\/sub>) jest okre\u015blona wzorem S<sub>n<\/sub>=2n<sup>2<\/sup>+n . Wtedy wyraz a<sub>2<\/sub> jest r\u00f3wny:<\/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) 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) 6<\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<p>c) 7<\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<p>d) 10<\/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_69e22b4968bcd\">\n        <button class=\"premium-btn-odp\"\n                data-id=\"odp_69e22b4968bcd\"\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) 3\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_69e22b4968bd8\">\n        <button class=\"premium-btn-wyjasnienie\"\n                data-id=\"wyjasnienie_69e22b4968bd8\"\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>Dana jest suma n pocz\u0105tkowych wyraz\u00f3w ci\u0105gu arytmetycznego:<\/p>\n\n<p><code>S\u2099 = 2n\u00b2 + n<\/code><\/p>\n\n<h3>Krok 1: Obliczenie a\u2082 ze wzoru na sum\u0119<\/h3>\n\n<p>Wiemy, \u017ce:<\/p>\n<p><code>S\u2081 = a\u2081<\/code><\/p>\n<p><code>S\u2082 = a\u2081 + a\u2082<\/code><\/p>\n\n<h3>Krok 2: Obliczenie S\u2081 i S\u2082<\/h3>\n\n<p>\nS\u2081 = 2\u00b71\u00b2 + 1 = 3<br>\nS\u2082 = 2\u00b72\u00b2 + 2 = 10\n<\/p>\n\n<h3>Krok 3: Wyznaczenie a\u2082<\/h3>\n\n<p>\na\u2082 = S\u2082 \u2212 S\u2081 = 10 \u2212 3 = <strong>3<\/strong>\n<\/p>\n\n<h3>Wniosek<\/h3>\n\n<p><strong>Wyraz a\u2082 jest r\u00f3wny 3.<\/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 sierpie\u0144 2016 (1 pkt) Dla ka\u017cdej liczby ca\u0142kowitej dodatniej n suma n pocz\u0105tkowych wyraz\u00f3w ci\u0105gu arytmetycznego (an) jest okre\u015blona wzorem Sn=2n2+n . Wtedy wyraz a2 jest r\u00f3wny: a) 3 b) 6 c) 7 d) 10<\/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":[25,204,70,81,83],"tags":[23,205,69],"class_list":["post-1472","post","type-post","status-publish","format-standard","hentry","category-ciag-arytmetyczny","category-rozne","category-sierpien-2016","category-zadania-maturalne","category-zadania-tematami","tag-ciag-arytmetyczny","tag-rozne","tag-sierpien-2016"],"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 sierpie\u0144 2016 (1 pkt) Dla ka\u017cdej liczby ca\u0142kowitej dodatniej n suma n pocz\u0105tkowych wyraz\u00f3w ci\u0105gu arytmetycznego (an) jest okre\u015blona wzorem Sn=2n2+n . Wtedy wyraz a2 jest r\u00f3wny: a) 3 b) 6 c) 7 d) 10","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/mymatma.pl\/index.php?rest_route=\/wp\/v2\/posts\/1472","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=1472"}],"version-history":[{"count":2,"href":"https:\/\/mymatma.pl\/index.php?rest_route=\/wp\/v2\/posts\/1472\/revisions"}],"predecessor-version":[{"id":1474,"href":"https:\/\/mymatma.pl\/index.php?rest_route=\/wp\/v2\/posts\/1472\/revisions\/1474"}],"wp:attachment":[{"href":"https:\/\/mymatma.pl\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1472"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mymatma.pl\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1472"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mymatma.pl\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1472"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}