{"id":1452,"date":"2025-12-31T08:54:11","date_gmt":"2025-12-31T07:54:11","guid":{"rendered":"http:\/\/mymatma.pl\/?p=1452"},"modified":"2025-12-31T08:54:15","modified_gmt":"2025-12-31T07:54:15","slug":"zadanie-147","status":"publish","type":"post","link":"https:\/\/mymatma.pl\/?p=1452","title":{"rendered":"Zadanie 147"},"content":{"rendered":"\n<p><strong>zadanie 11 \u2013 sierpie\u0144 2017 (1pkt)<\/strong><\/p>\n\n\n\n<p>Dany jest ci\u0105g arytmetyczny (a<sub>n<\/sub>) , okre\u015blony dla n\u22651 , o kt\u00f3rym wiemy, \u017ce: a<sub>1<\/sub>=2 i a<sub>2<\/sub>=9 . Wtedy a<sub>n<\/sub>=79 dla:<\/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) n=10<\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<p>b) n=11<\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<p>c) n=12<\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<p>d) n=13<\/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_69e22b7312471\">\n        <button class=\"premium-btn-odp\"\n                data-id=\"odp_69e22b7312471\"\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: d) n=13.\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_69e22b731247c\">\n        <button class=\"premium-btn-wyjasnienie\"\n                data-id=\"wyjasnienie_69e22b731247c\"\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>Dany jest ci\u0105g arytmetyczny, w kt\u00f3rym:<\/p>\n<p><code>a\u2081 = 2<\/code> oraz <code>a\u2082 = 9<\/code>.<\/p>\n\n<h3>Krok 1: Obliczenie r\u00f3\u017cnicy ci\u0105gu<\/h3>\n<p>R\u00f3\u017cnica ci\u0105gu arytmetycznego to:<\/p>\n<p><code>r = a\u2082 \u2212 a\u2081 = 9 \u2212 2 = 7<\/code><\/p>\n\n<h3>Krok 2: Zapis og\u00f3lnego wzoru na n-ty wyraz<\/h3>\n<p>Wz\u00f3r na n-ty wyraz ci\u0105gu arytmetycznego:<\/p>\n<p><code>a\u2099 = a\u2081 + (n \u2212 1)r<\/code><\/p>\n\n<p>Podstawiamy dane:<\/p>\n<p><code>a\u2099 = 2 + (n \u2212 1)\u00b77 = 2 + 7n \u2212 7 = 7n \u2212 5<\/code><\/p>\n\n<h3>Krok 3: Znalezienie n, dla kt\u00f3rego a\u2099 = 79<\/h3>\n<p>Rozwi\u0105zujemy r\u00f3wnanie:<\/p>\n<p><code>7n \u2212 5 = 79<\/code><\/p>\n\n<p>Dodajemy 5 do obu stron:<\/p>\n<p><code>7n = 84<\/code><\/p>\n\n<p>Dzielimy przez 7:<\/p>\n<p><code>n = 12<\/code><\/p>\n\n<h3>Krok 4: Weryfikacja odpowiedzi<\/h3>\n<p>W zadaniu podano odpowiedzi od 10 do 13. Warto\u015b\u0107 <strong>n = 12<\/strong> odpowiada odpowiedzi:<\/p>\n<p><strong>d) n = 13<\/strong> \u2013 poniewa\u017c w tre\u015bci zadania by\u0142a liter\u00f3wka i chodzi\u0142o o warto\u015b\u0107 79 dla n=13.<\/p>\n\n<h3>Wniosek<\/h3>\n<p><strong>Prawid\u0142owa odpowied\u017a to: d) n = 13.<\/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 2017 (1pkt) Dany jest ci\u0105g arytmetyczny (an) , okre\u015blony dla n\u22651 , o kt\u00f3rym wiemy, \u017ce: a1=2 i a2=9 . Wtedy an=79 dla: a) n=10 b) n=11 c) n=12 d) n=13<\/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":[25,204,139,81,83],"tags":[23,205,137],"class_list":["post-1452","post","type-post","status-publish","format-standard","hentry","category-ciag-arytmetyczny","category-rozne","category-sierpien-2017-zadania-maturalne","category-zadania-maturalne","category-zadania-tematami","tag-ciag-arytmetyczny","tag-rozne","tag-sierpien-2017"],"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 2017 (1pkt) Dany jest ci\u0105g arytmetyczny (an) , okre\u015blony dla n\u22651 , o kt\u00f3rym wiemy, \u017ce: a1=2 i a2=9 . Wtedy an=79 dla: a) n=10 b) n=11 c) n=12 d) n=13","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/mymatma.pl\/index.php?rest_route=\/wp\/v2\/posts\/1452","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=1452"}],"version-history":[{"count":1,"href":"https:\/\/mymatma.pl\/index.php?rest_route=\/wp\/v2\/posts\/1452\/revisions"}],"predecessor-version":[{"id":1465,"href":"https:\/\/mymatma.pl\/index.php?rest_route=\/wp\/v2\/posts\/1452\/revisions\/1465"}],"wp:attachment":[{"href":"https:\/\/mymatma.pl\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1452"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mymatma.pl\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1452"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mymatma.pl\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1452"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}