{"id":1119,"date":"2025-12-18T10:26:36","date_gmt":"2025-12-18T09:26:36","guid":{"rendered":"http:\/\/mymatma.pl\/?p=1119"},"modified":"2025-12-18T12:39:12","modified_gmt":"2025-12-18T11:39:12","slug":"zadanie-77","status":"publish","type":"post","link":"https:\/\/mymatma.pl\/?p=1119","title":{"rendered":"Zadanie 77"},"content":{"rendered":"\n<p><strong>zadanie 16 \u2013 sierpie\u0144 2025 (1pkt)<\/strong><\/p>\n\n\n\n<p>Ci\u0105g arytmetyczny (a<sub>n<\/sub>) jest okre\u015blony dla ka\u017cdej liczby naturalnej n\u22651 . R\u00f3\u017cnica tego ci\u0105gu jest r\u00f3wna (\u22124) oraz a<sub>10<\/sub>=\u221224 . Sz\u00f3sty wyraz ci\u0105gu (a<sub>n<\/sub>) jest r\u00f3wny:<\/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) -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) -8<\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\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>c) -4<\/p>\n<\/div>\n<\/div>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<p>d) 0<\/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_69e228102914d\">\n        <button class=\"premium-btn-odp\"\n                data-id=\"odp_69e228102914d\"\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            \n<b>b) -8<\/b>\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_69e2281029158\">\n        <button class=\"premium-btn-wyjasnienie\"\n                data-id=\"wyjasnienie_69e2281029158\"\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>\nCi\u0105g arytmetyczny ma sta\u0142\u0105 r\u00f3\u017cnic\u0119 <strong>r = -4<\/strong>.  \nAby znale\u017a\u0107 sz\u00f3sty wyraz, korzystamy ze wzoru na n\u2011ty wyraz ci\u0105gu arytmetycznego:\n<br><br>\na<sub>n<\/sub> = a<sub>1<\/sub> + (n \u2212 1)r\n<br><br>\nWiemy, \u017ce:\n<br>\na<sub>10<\/sub> = a<sub>1<\/sub> + 9r = -24\n<br>\na<sub>1<\/sub> + 9 \u00b7 (-4) = -24\n<br>\na<sub>1<\/sub> &#8211; 36 = -24\n<br>\na<sub>1<\/sub> = 12\n<br><br>\nTeraz obliczamy a<sub>6<\/sub>:\n<br>\na<sub>6<\/sub> = a<sub>1<\/sub> + 5r = 12 + 5 \u00b7 (-4) = -8\n<br><br>\n<strong>Odpowied\u017a: b) -8<\/strong>\n<\/p>\n\n        <\/div>\n    <\/div>\n    \n<\/div>\n<\/div>\n\n\n\n<p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>zadanie 16 \u2013 sierpie\u0144 2025 (1pkt) Ci\u0105g arytmetyczny (an) jest okre\u015blony dla ka\u017cdej liczby naturalnej n\u22651 . R\u00f3\u017cnica tego ci\u0105gu jest r\u00f3wna (\u22124) oraz a10=\u221224 . Sz\u00f3sty wyraz ci\u0105gu (an) jest r\u00f3wny: a) -12 b) -8 c) -4 d) 0<\/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":[25,26,50,81,83],"tags":[23,24,51],"class_list":["post-1119","post","type-post","status-publish","format-standard","hentry","category-ciag-arytmetyczny","category-obliczanie-wyrazow-ciagu","category-sierpien-2025","category-zadania-maturalne","category-zadania-tematami","tag-ciag-arytmetyczny","tag-obliczanie-wyrazow-ciagu","tag-sierpien-2025"],"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 16 \u2013 sierpie\u0144 2025 (1pkt) Ci\u0105g arytmetyczny (an) jest okre\u015blony dla ka\u017cdej liczby naturalnej n\u22651 . R\u00f3\u017cnica tego ci\u0105gu jest r\u00f3wna (\u22124) oraz a10=\u221224 . Sz\u00f3sty wyraz ci\u0105gu (an) jest r\u00f3wny: a) -12 b) -8 c) -4 d) 0","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/mymatma.pl\/index.php?rest_route=\/wp\/v2\/posts\/1119","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=1119"}],"version-history":[{"count":2,"href":"https:\/\/mymatma.pl\/index.php?rest_route=\/wp\/v2\/posts\/1119\/revisions"}],"predecessor-version":[{"id":1149,"href":"https:\/\/mymatma.pl\/index.php?rest_route=\/wp\/v2\/posts\/1119\/revisions\/1149"}],"wp:attachment":[{"href":"https:\/\/mymatma.pl\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1119"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mymatma.pl\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1119"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mymatma.pl\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1119"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}