{"id":1175,"date":"2025-12-18T14:45:14","date_gmt":"2025-12-18T13:45:14","guid":{"rendered":"http:\/\/mymatma.pl\/?p=1175"},"modified":"2025-12-18T14:45:17","modified_gmt":"2025-12-18T13:45:17","slug":"zadanie-92","status":"publish","type":"post","link":"https:\/\/mymatma.pl\/?p=1175","title":{"rendered":"Zadanie 92"},"content":{"rendered":"\n<p><strong>zadanie 20 \u2013 czerwiec 2013 (1pkt)<\/strong><\/p>\n\n\n\n<p>Dany jest ci\u0105g arytmetyczny (a<sub>n<\/sub>) w kt\u00f3rym r\u00f3\u017cnica r=\u22122 oraz a<sub>20<\/sub>=17 . W\u00f3wczas pierwszy wyraz tego ci\u0105gu 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) 45<\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<p>b) 50<\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<p>c) 55<\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<p>d) 60<\/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_69e22bed1e745\">\n        <button class=\"premium-btn-odp\"\n                data-id=\"odp_69e22bed1e745\"\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) 60.\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_69e22bed1e752\">\n        <button class=\"premium-btn-wyjasnienie\"\n                data-id=\"wyjasnienie_69e22bed1e752\"\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<p>\n  W zadaniu podano, \u017ce r\u00f3\u017cnica ci\u0105gu arytmetycznego wynosi <em>r = -2<\/em> oraz \u017ce\n  dwudziesty wyraz ci\u0105gu jest r\u00f3wny <em>a\u208d20\u208e = 17<\/em>.\n<\/p>\n\n<p>\n  Korzystamy ze wzoru na n-ty wyraz ci\u0105gu arytmetycznego:\n  <br>\n  a\u2099 = a\u2081 + (n \u2212 1) \u00b7 r\n<\/p>\n\n<p>\n  Podstawiamy dane do wzoru dla n = 20:\n  <br>\n  17 = a\u2081 + 19 \u00b7 (\u22122)\n<\/p>\n\n<p>\n  Obliczamy:\n  <br>\n  17 = a\u2081 \u2212 38\n<\/p>\n\n<p>\n  Dodajemy 38 do obu stron r\u00f3wnania:\n  <br>\n  a\u2081 = 17 + 38 = 55\n<\/p>\n\n<p>\n  Pierwszy wyraz ci\u0105gu wynosi wi\u0119c <strong>55<\/strong>.\n<\/p>\n\n<p>\n  Odpowied\u017a: <strong>c)<\/strong>\n<\/p>\n\n        <\/div>\n    <\/div>\n    \n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>zadanie 20 \u2013 czerwiec 2013 (1pkt) Dany jest ci\u0105g arytmetyczny (an) w kt\u00f3rym r\u00f3\u017cnica r=\u22122 oraz a20=17 . W\u00f3wczas pierwszy wyraz tego ci\u0105gu jest r\u00f3wny: a) 45 b) 50 c) 55 d) 60<\/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":[25,78,26,81,83],"tags":[23,77,24],"class_list":["post-1175","post","type-post","status-publish","format-standard","hentry","category-ciag-arytmetyczny","category-czerwiec-2013","category-obliczanie-wyrazow-ciagu","category-zadania-maturalne","category-zadania-tematami","tag-ciag-arytmetyczny","tag-czerwiec-2013","tag-obliczanie-wyrazow-ciagu"],"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 20 \u2013 czerwiec 2013 (1pkt) Dany jest ci\u0105g arytmetyczny (an) w kt\u00f3rym r\u00f3\u017cnica r=\u22122 oraz a20=17 . W\u00f3wczas pierwszy wyraz tego ci\u0105gu jest r\u00f3wny: a) 45 b) 50 c) 55 d) 60","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/mymatma.pl\/index.php?rest_route=\/wp\/v2\/posts\/1175","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=1175"}],"version-history":[{"count":1,"href":"https:\/\/mymatma.pl\/index.php?rest_route=\/wp\/v2\/posts\/1175\/revisions"}],"predecessor-version":[{"id":1176,"href":"https:\/\/mymatma.pl\/index.php?rest_route=\/wp\/v2\/posts\/1175\/revisions\/1176"}],"wp:attachment":[{"href":"https:\/\/mymatma.pl\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1175"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mymatma.pl\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1175"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mymatma.pl\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1175"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}