{"id":1193,"date":"2025-12-19T09:52:18","date_gmt":"2025-12-19T08:52:18","guid":{"rendered":"https:\/\/mymatma.pl\/?p=1193"},"modified":"2025-12-19T09:52:21","modified_gmt":"2025-12-19T08:52:21","slug":"zadanie-100","status":"publish","type":"post","link":"https:\/\/mymatma.pl\/?p=1193","title":{"rendered":"Zadanie 100"},"content":{"rendered":"\n<p><strong>zadanie 14 \u2013 czerwiec 2018 (1pkt)<\/strong><\/p>\n\n\n\n<p>Dany jest ci\u0105g arytmetyczny (a<sub>n<\/sub>) okre\u015blony wzorem a<sub>n<\/sub>=16\u221212\u22c5n dla ka\u017cdej liczby ca\u0142kowitej n\u22651 . R\u00f3\u017cnica r 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) r = -16<\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<p>b) r = -(1\/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) r = -(1\/32)<\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<p>d) r = 15\u00bd<\/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_69e22b40c8cb0\">\n        <button class=\"premium-btn-odp\"\n                data-id=\"odp_69e22b40c8cb0\"\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) r = -12.\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_69e22b40c8cbb\">\n        <button class=\"premium-btn-wyjasnienie\"\n                data-id=\"wyjasnienie_69e22b40c8cbb\"\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 czerwiec 2018<\/h3>\n<ol>\n  <li>\n    <strong>Dany wz\u00f3r ci\u0105gu:<\/strong><br>\n    a<sub>n<\/sub> = 16 \u2212 12\u00b7n\n  <\/li>\n  <li>\n    <strong>R\u00f3\u017cnica ci\u0105gu arytmetycznego:<\/strong><br>\n    r = a<sub>n+1<\/sub> \u2212 a<sub>n<\/sub>\n  <\/li>\n  <li>\n    <strong>Obliczenia:<\/strong><br>\n    a<sub>n+1<\/sub> = 16 \u2212 12(n+1) = 16 \u2212 12n \u2212 12 = 4 \u2212 12n<br>\n    a<sub>n<\/sub> = 16 \u2212 12n<br>\n    r = (4 \u2212 12n) \u2212 (16 \u2212 12n) = 4 \u2212 12n \u2212 16 + 12n = -12\n  <\/li>\n  <li>\n    <strong>Wniosek:<\/strong><br>\n    R\u00f3\u017cnica ci\u0105gu arytmetycznego wynosi <u>-12<\/u>.\n  <\/li>\n<\/ol>\n<p><strong>Uwaga:<\/strong> W podanych odpowiedziach nie ma warto\u015bci -12, wi\u0119c prawid\u0142owa r\u00f3\u017cnica to -12, a zadanie zawiera b\u0142\u0105d w opcjach.<\/p>\n\n        <\/div>\n    <\/div>\n    \n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>zadanie 14 \u2013 czerwiec 2018 (1pkt) Dany jest ci\u0105g arytmetyczny (an) okre\u015blony wzorem an=16\u221212\u22c5n dla ka\u017cdej liczby ca\u0142kowitej n\u22651 . R\u00f3\u017cnica r tego ci\u0105gu jest r\u00f3wna: a) r = -16 b) r = -(1\/2) c) r = -(1\/32) d) r = 15\u00bd<\/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":[25,68,160,81,83],"tags":[23,67,161],"class_list":["post-1193","post","type-post","status-publish","format-standard","hentry","category-ciag-arytmetyczny","category-czerwiec-2018","category-obliczanie-roznicy-ciagu","category-zadania-maturalne","category-zadania-tematami","tag-ciag-arytmetyczny","tag-czerwiec-2018","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 14 \u2013 czerwiec 2018 (1pkt) Dany jest ci\u0105g arytmetyczny (an) okre\u015blony wzorem an=16\u221212\u22c5n dla ka\u017cdej liczby ca\u0142kowitej n\u22651 . R\u00f3\u017cnica r tego ci\u0105gu jest r\u00f3wna: a) r = -16 b) r = -(1\/2) c) r = -(1\/32) d) r = 15\u00bd","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/mymatma.pl\/index.php?rest_route=\/wp\/v2\/posts\/1193","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=1193"}],"version-history":[{"count":1,"href":"https:\/\/mymatma.pl\/index.php?rest_route=\/wp\/v2\/posts\/1193\/revisions"}],"predecessor-version":[{"id":1194,"href":"https:\/\/mymatma.pl\/index.php?rest_route=\/wp\/v2\/posts\/1193\/revisions\/1194"}],"wp:attachment":[{"href":"https:\/\/mymatma.pl\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1193"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mymatma.pl\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1193"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mymatma.pl\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1193"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}