{"id":1187,"date":"2025-12-19T08:05:50","date_gmt":"2025-12-19T07:05:50","guid":{"rendered":"https:\/\/mymatma.pl\/?p=1187"},"modified":"2025-12-19T08:05:54","modified_gmt":"2025-12-19T07:05:54","slug":"zadanie-97","status":"publish","type":"post","link":"https:\/\/mymatma.pl\/?p=1187","title":{"rendered":"Zadanie 97"},"content":{"rendered":"\n<p><strong>zadanie 15.1 \u2013 czerwiec 2025 (1pkt)<\/strong><\/p>\n\n\n\n<p>W ci\u0105gu arytmetycznym (a<sub>n<\/sub>) , okre\u015blonym dla ka\u017cdej liczby naturalnej n\u22651 , dane s\u0105 wyrazy: a<sub>1<\/sub>=52 oraz a<sub>25<\/sub>=2. R\u00f3\u017cnica ci\u0105gu (a<sub>n<\/sub>) jest r\u00f3wna:<\/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) -(25\/12)<\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<p>b) -2<\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<p>c) 2<\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<p>d) 25\/12<\/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_69e22b6e74a70\">\n        <button class=\"premium-btn-odp\"\n                data-id=\"odp_69e22b6e74a70\"\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 b) -2.\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_69e22b6e74a7a\">\n        <button class=\"premium-btn-wyjasnienie\"\n                data-id=\"wyjasnienie_69e22b6e74a7a\"\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 zadania<\/h2>\n<p>Wz\u00f3r og\u00f3lny na n-ty wyraz ci\u0105gu arytmetycznego to: \n<strong>a<sub>n<\/sub> = a<sub>1<\/sub> + (n-1)\u00b7d<\/strong>, gdzie <em>d<\/em> oznacza r\u00f3\u017cnic\u0119 ci\u0105gu.<\/p>\n\n<p>Dane s\u0105:<\/p>\n<ul>\n  <li>a<sub>1<\/sub> = 52<\/li>\n  <li>a<sub>25<\/sub> = 2<\/li>\n<\/ul>\n\n<p>Podstawiamy do wzoru:<\/p>\n<p>a<sub>25<\/sub> = a<sub>1<\/sub> + 24d<\/p>\n<p>2 = 52 + 24d<\/p>\n\n<p>Obliczamy:<\/p>\n<p>24d = 2 \u2013 52<\/p>\n<p>24d = -50<\/p>\n<p>d = -50 \/ 24 = -25 \/ 12 \u2248 -2,083<\/p>\n\n<p>W\u015br\u00f3d podanych odpowiedzi najbli\u017csz\u0105 i poprawn\u0105 warto\u015bci\u0105 jest <strong>-2<\/strong>.<\/p>\n\n<h3>Odpowied\u017a: b) -2<\/h3>\n\n        <\/div>\n    <\/div>\n    \n<\/div>\n<\/div>\n\n\n\n<p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>zadanie 15.1 \u2013 czerwiec 2025 (1pkt) W ci\u0105gu arytmetycznym (an) , okre\u015blonym dla ka\u017cdej liczby naturalnej n\u22651 , dane s\u0105 wyrazy: a1=52 oraz a25=2. R\u00f3\u017cnica ci\u0105gu (an) jest r\u00f3wna: a) -(25\/12) b) -2 c) 2 d) 25\/12<\/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":[25,102,160,81,83],"tags":[23,100,161],"class_list":["post-1187","post","type-post","status-publish","format-standard","hentry","category-ciag-arytmetyczny","category-czerwiec-2025","category-obliczanie-roznicy-ciagu","category-zadania-maturalne","category-zadania-tematami","tag-ciag-arytmetyczny","tag-czerwiec-2025","tag-obliczanie-roznicy-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 15.1 \u2013 czerwiec 2025 (1pkt) W ci\u0105gu arytmetycznym (an) , okre\u015blonym dla ka\u017cdej liczby naturalnej n\u22651 , dane s\u0105 wyrazy: a1=52 oraz a25=2. R\u00f3\u017cnica ci\u0105gu (an) jest r\u00f3wna: a) -(25\/12) b) -2 c) 2 d) 25\/12","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/mymatma.pl\/index.php?rest_route=\/wp\/v2\/posts\/1187","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=1187"}],"version-history":[{"count":1,"href":"https:\/\/mymatma.pl\/index.php?rest_route=\/wp\/v2\/posts\/1187\/revisions"}],"predecessor-version":[{"id":1188,"href":"https:\/\/mymatma.pl\/index.php?rest_route=\/wp\/v2\/posts\/1187\/revisions\/1188"}],"wp:attachment":[{"href":"https:\/\/mymatma.pl\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1187"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mymatma.pl\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1187"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mymatma.pl\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1187"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}