{"id":1177,"date":"2025-12-18T14:51:07","date_gmt":"2025-12-18T13:51:07","guid":{"rendered":"http:\/\/mymatma.pl\/?p=1177"},"modified":"2025-12-18T14:51:12","modified_gmt":"2025-12-18T13:51:12","slug":"zadanie-93","status":"publish","type":"post","link":"https:\/\/mymatma.pl\/?p=1177","title":{"rendered":"Zadanie 93"},"content":{"rendered":"\n<p><strong>zadanie 13 \u2013 maj 2013 (1pkt)<\/strong><\/p>\n\n\n\n<p>Ci\u0105g (a<sub>n<\/sub>) okre\u015blony dla n\u22651 jest arytmetyczny oraz a<sub>3<\/sub>=10 i a<sub>4<\/sub>=14 . Pierwszy wyraz tego ci\u0105gu 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) a<sub>1<\/sub> = -2<\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<p>b) a<sub>1<\/sub> = 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) a<sub>1<\/sub> = 6<\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<p>d) a<sub>1<\/sub> = 12<\/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_69e22b9c351a5\">\n        <button class=\"premium-btn-odp\"\n                data-id=\"odp_69e22b9c351a5\"\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) a1 = 6.\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_69e22b9c351b0\">\n        <button class=\"premium-btn-wyjasnienie\"\n                data-id=\"wyjasnienie_69e22b9c351b0\"\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>\n  W zadaniu podano dwa kolejne wyrazy ci\u0105gu arytmetycznego:\n  <br>\n  a\u2083 = 10 oraz a\u2084 = 14.\n<\/p>\n\n<p>\n  R\u00f3\u017cnic\u0119 ci\u0105gu obliczamy jako r\u00f3\u017cnic\u0119 kolejnych wyraz\u00f3w:\n  <br>\n  r = a\u2084 \u2212 a\u2083 = 14 \u2212 10 = 4\n<\/p>\n\n<p>\n  Korzystamy ze wzoru na n-ty wyraz ci\u0105gu arytmetycznego:\n  <br>\n  a\u2099 = a\u2081 + (n \u2212 1) \u00b7 r\n<\/p>\n\n<p>\n  Podstawiamy dane dla a\u2083:\n  <br>\n  10 = a\u2081 + 2 \u00b7 4\n<\/p>\n\n<p>\n  Obliczamy:\n  <br>\n  10 = a\u2081 + 8\n  <br>\n  a\u2081 = 10 \u2212 8 = 2\n<\/p>\n\n<p>\n  Pierwszy wyraz ci\u0105gu wynosi wi\u0119c <strong>6<\/strong>.\n<\/p>\n\n<p>\n  Odpowied\u017a: <strong>c)<\/strong>\n<\/p>\n\n        <\/div>\n    <\/div>\n    \n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>zadanie 13 \u2013 maj 2013 (1pkt) Ci\u0105g (an) okre\u015blony dla n\u22651 jest arytmetyczny oraz a3=10 i a4=14 . Pierwszy wyraz tego ci\u0105gu jest r\u00f3wny: a) a1 = -2 b) a1 = 2 c) a1 = 6 d) a1 = 12<\/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":[25,126,26,81,83],"tags":[23,125,24],"class_list":["post-1177","post","type-post","status-publish","format-standard","hentry","category-ciag-arytmetyczny","category-maj-2013","category-obliczanie-wyrazow-ciagu","category-zadania-maturalne","category-zadania-tematami","tag-ciag-arytmetyczny","tag-maj-2013","tag-obliczanie-wyrazow-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 \u2013 maj 2013 (1pkt) Ci\u0105g (an) okre\u015blony dla n\u22651 jest arytmetyczny oraz a3=10 i a4=14 . Pierwszy wyraz tego ci\u0105gu jest r\u00f3wny: a) a1 = -2 b) a1 = 2 c) a1 = 6 d) a1 = 12","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/mymatma.pl\/index.php?rest_route=\/wp\/v2\/posts\/1177","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=1177"}],"version-history":[{"count":1,"href":"https:\/\/mymatma.pl\/index.php?rest_route=\/wp\/v2\/posts\/1177\/revisions"}],"predecessor-version":[{"id":1178,"href":"https:\/\/mymatma.pl\/index.php?rest_route=\/wp\/v2\/posts\/1177\/revisions\/1178"}],"wp:attachment":[{"href":"https:\/\/mymatma.pl\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1177"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mymatma.pl\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1177"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mymatma.pl\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1177"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}