{"id":1189,"date":"2025-12-19T09:40:52","date_gmt":"2025-12-19T08:40:52","guid":{"rendered":"https:\/\/mymatma.pl\/?p=1189"},"modified":"2025-12-19T09:40:56","modified_gmt":"2025-12-19T08:40:56","slug":"zadanie-98","status":"publish","type":"post","link":"https:\/\/mymatma.pl\/?p=1189","title":{"rendered":"Zadanie 98"},"content":{"rendered":"\n<p><strong>zadanie 14 \u2013 maj 2022 (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 , a<sub>5<\/sub>=\u221231 oraz a<sub>10<\/sub>=\u221266 . R\u00f3\u017cnica tego ci\u0105gu 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) -7<\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<p>b) -19,4<\/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) 19,4<\/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_69e22ab95c964\">\n        <button class=\"premium-btn-odp\"\n                data-id=\"odp_69e22ab95c964\"\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) -7.\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_69e22ab95c970\">\n        <button class=\"premium-btn-wyjasnienie\"\n                data-id=\"wyjasnienie_69e22ab95c970\"\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 zadania 14 \u2014 maj 2022<\/h3>\n<ol>\n  <li>\n    <strong>Wz\u00f3r og\u00f3lny ci\u0105gu arytmetycznego:<\/strong>\n    <br>\n    \n\n\\[a_n = a_1 + (n &#8211; 1)\\cdot r\\]\n\n\n  <\/li>\n  <li>\n    <strong>Skorzystaj z r\u00f3\u017cnicy dw\u00f3ch wyraz\u00f3w:<\/strong>\n    <br>\n    \n\n\\[a_{10} &#8211; a_5 = \\big(a_1 + 9r\\big) &#8211; \\big(a_1 + 4r\\big) = 5r\\]\n\n\n  <\/li>\n  <li>\n    <strong>Podstaw dane z tre\u015bci zadania:<\/strong>\n    <br>\n    \n\n\\[-66 &#8211; (-31) = -66 + 31 = -35\\]\n\n\n    <br>\n    \n\n\\[5r = -35\\]\n\n\n  <\/li>\n  <li>\n    <strong>Oblicz r\u00f3\u017cnic\u0119 ci\u0105gu:<\/strong>\n    <br>\n    \n\n\\[r = \\frac{-35}{5} = -7\\]\n\n\n  <\/li>\n<\/ol>\n<p><strong>Wniosek:<\/strong> R\u00f3\u017cnica ci\u0105gu arytmetycznego wynosi \\(-7\\), czyli odpowied\u017a A.<\/p>\n\n        <\/div>\n    <\/div>\n    \n<\/div>\n<\/div>\n\n\n\n<p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>zadanie 14 \u2013 maj 2022 (1pkt) W ci\u0105gu arytmetycznym (an) , okre\u015blonym dla ka\u017cdej liczby naturalnej n\u22651 , a5=\u221231 oraz a10=\u221266 . R\u00f3\u017cnica tego ci\u0105gu jest r\u00f3wna: a) -7 b) -19,4 c) 7 d) 19,4<\/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":[25,58,160,81,83],"tags":[23,57,162],"class_list":["post-1189","post","type-post","status-publish","format-standard","hentry","category-ciag-arytmetyczny","category-maj-2022","category-obliczanie-roznicy-ciagu","category-zadania-maturalne","category-zadania-tematami","tag-ciag-arytmetyczny","tag-maj-2022","tag-obliczanie-roznicy-ciacu"],"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 14 \u2013 maj 2022 (1pkt) W ci\u0105gu arytmetycznym (an) , okre\u015blonym dla ka\u017cdej liczby naturalnej n\u22651 , a5=\u221231 oraz a10=\u221266 . R\u00f3\u017cnica tego ci\u0105gu jest r\u00f3wna: a) -7 b) -19,4 c) 7 d) 19,4","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/mymatma.pl\/index.php?rest_route=\/wp\/v2\/posts\/1189","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=1189"}],"version-history":[{"count":1,"href":"https:\/\/mymatma.pl\/index.php?rest_route=\/wp\/v2\/posts\/1189\/revisions"}],"predecessor-version":[{"id":1190,"href":"https:\/\/mymatma.pl\/index.php?rest_route=\/wp\/v2\/posts\/1189\/revisions\/1190"}],"wp:attachment":[{"href":"https:\/\/mymatma.pl\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1189"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mymatma.pl\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1189"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mymatma.pl\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1189"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}