{"id":1182,"date":"2025-12-19T07:46:01","date_gmt":"2025-12-19T06:46:01","guid":{"rendered":"https:\/\/mymatma.pl\/?p=1182"},"modified":"2025-12-19T07:46:34","modified_gmt":"2025-12-19T06:46:34","slug":"zadanie-95","status":"publish","type":"post","link":"https:\/\/mymatma.pl\/?p=1182","title":{"rendered":"Zadanie 95"},"content":{"rendered":"\n<p><strong>zadanie 14 \u2013 sierpie\u0144 2010 (1pkt)<\/strong><\/p>\n\n\n\n<p>W ci\u0105gu arytmetycznym (a<sub>n<\/sub>) mamy: a<sub>2<\/sub>=5 i a<sub>4<\/sub>=11 . Oblicz a<sub>5<\/sub>.<\/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) 8<\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<p>b) 14<\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<p>c) 17<\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<p>d) 6<\/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_69e22b93ee9b3\">\n        <button class=\"premium-btn-odp\"\n                data-id=\"odp_69e22b93ee9b3\"\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\u0142owy wynik to b) 14.\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_69e22b93ee9bf\">\n        <button class=\"premium-btn-wyjasnienie\"\n                data-id=\"wyjasnienie_69e22b93ee9bf\"\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>W ci\u0105gu arytmetycznym ka\u017cdy wyraz r\u00f3\u017cni si\u0119 od poprzedniego o sta\u0142\u0105 warto\u015b\u0107 \u2013 r\u00f3\u017cnic\u0119 ci\u0105gu (oznaczamy j\u0105 jako <em>d<\/em>).<\/p>\n\n<p>Wiemy, \u017ce:<\/p>\n<ul>\n  <li>a<sub>2<\/sub> = 5<\/li>\n  <li>a<sub>4<\/sub> = 11<\/li>\n<\/ul>\n\n<p>Skorzystajmy ze wzoru og\u00f3lnego: <strong>a<sub>n<\/sub> = a<sub>1<\/sub> + (n-1)\u00b7d<\/strong>.<\/p>\n\n<p>Podstawiaj\u0105c dane:<\/p>\n<ul>\n  <li>a<sub>2<\/sub> = a<sub>1<\/sub> + d = 5<\/li>\n  <li>a<sub>4<\/sub> = a<sub>1<\/sub> + 3d = 11<\/li>\n<\/ul>\n\n<p>Odejmujemy r\u00f3wnania:<\/p>\n<p>(a<sub>1<\/sub> + 3d) \u2013 (a<sub>1<\/sub> + d) = 11 \u2013 5<\/p>\n<p>2d = 6 \u21d2 d = 3<\/p>\n\n<p>Teraz obliczamy a<sub>5<\/sub>:<\/p>\n<p>a<sub>5<\/sub> = a<sub>1<\/sub> + 4d<\/p>\n\n<p>Z pierwszego r\u00f3wnania: a<sub>1<\/sub> = 5 \u2013 d = 5 \u2013 3 = 2<\/p>\n<p>a<sub>5<\/sub> = 2 + 4\u00b73 = 2 + 12 = <strong>14<\/strong><\/p>\n\n<h3>Odpowied\u017a: b) 14<\/h3>\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 sierpie\u0144 2010 (1pkt) W ci\u0105gu arytmetycznym (an) mamy: a2=5 i a4=11 . Oblicz a5. a) 8 b) 14 c) 17 d) 6<\/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":[25,26,80,81,83],"tags":[23,24,79],"class_list":["post-1182","post","type-post","status-publish","format-standard","hentry","category-ciag-arytmetyczny","category-obliczanie-wyrazow-ciagu","category-sierpien-2010","category-zadania-maturalne","category-zadania-tematami","tag-ciag-arytmetyczny","tag-obliczanie-wyrazow-ciagu","tag-sierpien-2010"],"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 sierpie\u0144 2010 (1pkt) W ci\u0105gu arytmetycznym (an) mamy: a2=5 i a4=11 . Oblicz a5. a) 8 b) 14 c) 17 d) 6","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/mymatma.pl\/index.php?rest_route=\/wp\/v2\/posts\/1182","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=1182"}],"version-history":[{"count":2,"href":"https:\/\/mymatma.pl\/index.php?rest_route=\/wp\/v2\/posts\/1182\/revisions"}],"predecessor-version":[{"id":1184,"href":"https:\/\/mymatma.pl\/index.php?rest_route=\/wp\/v2\/posts\/1182\/revisions\/1184"}],"wp:attachment":[{"href":"https:\/\/mymatma.pl\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1182"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mymatma.pl\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1182"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mymatma.pl\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1182"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}