{"id":1240,"date":"2025-12-22T11:07:44","date_gmt":"2025-12-22T10:07:44","guid":{"rendered":"http:\/\/mymatma.pl\/?p=1240"},"modified":"2025-12-22T11:07:47","modified_gmt":"2025-12-22T10:07:47","slug":"zadanie-102","status":"publish","type":"post","link":"https:\/\/mymatma.pl\/?p=1240","title":{"rendered":"Zadanie 102"},"content":{"rendered":"\n<p><strong>zadanie 13 marzec 2012 (1pkt)<\/strong><\/p>\n\n\n\n<p>Ci\u0105g arytmetyczny (a<sub>n<\/sub>) jest okre\u015blony wzorem a<sub>n<\/sub>=\u22122n+1 dla n\u22651 . 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) -1<\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<p>b) 1<\/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) 3<\/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_69e22beba310b\">\n        <button class=\"premium-btn-odp\"\n                data-id=\"odp_69e22beba310b\"\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 c)-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_69e22beba3116\">\n        <button class=\"premium-btn-wyjasnienie\"\n                data-id=\"wyjasnienie_69e22beba3116\"\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>Aby obliczy\u0107 r\u00f3\u017cnic\u0119 ci\u0105gu arytmetycznego, korzystamy z faktu, \u017ce r\u00f3\u017cnica r to przyrost mi\u0119dzy kolejnymi wyrazami:<\/p>\n\n<p style=\"text-align:center;\">\nr = a<sub>n+1<\/sub> \u2212 a<sub>n<\/sub>\n<\/p>\n\n<p>W zadaniu dany jest wz\u00f3r og\u00f3lny ci\u0105gu:<\/p>\n\n<p style=\"text-align:center;\">\na<sub>n<\/sub> = -2n + 1\n<\/p>\n\n<p>Obliczamy dwa kolejne wyrazy:<\/p>\n\n<ul>\n  <li>a<sub>n<\/sub> = -2n + 1<\/li>\n  <li>a<sub>n+1<\/sub> = -2(n+1) + 1 = -2n &#8211; 2 + 1 = -2n &#8211; 1<\/li>\n<\/ul>\n\n<p>Teraz obliczamy r\u00f3\u017cnic\u0119:<\/p>\n\n<p style=\"text-align:center;\">\nr = a<sub>n+1<\/sub> \u2212 a<sub>n<\/sub> = (-2n &#8211; 1) \u2212 (-2n + 1)\n<\/p>\n\n<p>Upraszczamy wyra\u017cenie:<\/p>\n\n<p style=\"text-align:center;\">\nr = -2n &#8211; 1 + 2n &#8211; 1 = -2\n<\/p>\n\n<p>Ostatecznie r\u00f3\u017cnica ci\u0105gu wynosi:<\/p>\n\n<p style=\"text-align:center; font-size: 1.2em;\">\n<strong>r = -2<\/strong>\n<\/p>\n\n<p>Odpowied\u017a: <strong>c) -2<\/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 13 marzec 2012 (1pkt) Ci\u0105g arytmetyczny (an) jest okre\u015blony wzorem an=\u22122n+1 dla n\u22651 . R\u00f3\u017cnica tego ci\u0105gu jest r\u00f3wna: a) -1 b) 1 c) -2 d) 3<\/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":[25,42,160,81,83],"tags":[23,41,161],"class_list":["post-1240","post","type-post","status-publish","format-standard","hentry","category-ciag-arytmetyczny","category-marzec-2012","category-obliczanie-roznicy-ciagu","category-zadania-maturalne","category-zadania-tematami","tag-ciag-arytmetyczny","tag-marzec-2012","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 13 marzec 2012 (1pkt) Ci\u0105g arytmetyczny (an) jest okre\u015blony wzorem an=\u22122n+1 dla n\u22651 . R\u00f3\u017cnica tego ci\u0105gu jest r\u00f3wna: a) -1 b) 1 c) -2 d) 3","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/mymatma.pl\/index.php?rest_route=\/wp\/v2\/posts\/1240","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=1240"}],"version-history":[{"count":1,"href":"https:\/\/mymatma.pl\/index.php?rest_route=\/wp\/v2\/posts\/1240\/revisions"}],"predecessor-version":[{"id":1241,"href":"https:\/\/mymatma.pl\/index.php?rest_route=\/wp\/v2\/posts\/1240\/revisions\/1241"}],"wp:attachment":[{"href":"https:\/\/mymatma.pl\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1240"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mymatma.pl\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1240"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mymatma.pl\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1240"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}