{"id":1171,"date":"2025-12-18T14:36:22","date_gmt":"2025-12-18T13:36:22","guid":{"rendered":"http:\/\/mymatma.pl\/?p=1171"},"modified":"2025-12-18T14:36:24","modified_gmt":"2025-12-18T13:36:24","slug":"zadanie-90","status":"publish","type":"post","link":"https:\/\/mymatma.pl\/?p=1171","title":{"rendered":"Zadanie 90"},"content":{"rendered":"\n<p><strong>zadanie 14 \u2013 sierpie\u0144 2015 (1pkt)<\/strong><\/p>\n\n\n\n<p>Wszystkie dwucyfrowe liczby naturalne podzielne przez 7 tworz\u0105 rosn\u0105cy ci\u0105g arytmetyczny. Dwunastym wyrazem tego ci\u0105gu jest liczba:<\/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) 77<\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<p>b) 84<\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<p>c) 91<\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<p>d) 98<\/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_69e22b9f61601\">\n        <button class=\"premium-btn-odp\"\n                data-id=\"odp_69e22b9f61601\"\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) 91.\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_69e22b9f6160c\">\n        <button class=\"premium-btn-wyjasnienie\"\n                data-id=\"wyjasnienie_69e22b9f6160c\"\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  Wszystkie dwucyfrowe liczby naturalne podzielne przez 7 tworz\u0105 ci\u0105g arytmetyczny:\n  14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84, 91, &#8230;\n<\/p>\n<p>\n  Pierwszy wyraz ci\u0105gu to 14, a r\u00f3\u017cnica ci\u0105gu wynosi 7 (ka\u017cda kolejna liczba jest wi\u0119ksza o 7).\n<\/p>\n<p>\n  Korzystamy ze wzoru na n-ty wyraz ci\u0105gu arytmetycznego:\n  <br>\n  a<sub>n<\/sub> = a<sub>1<\/sub> + (n \u2212 1) &middot; r\n<\/p>\n<p>\n  Podstawiamy:\n  <br>\n  a<sub>1<\/sub> = 14, r = 7, n = 12\n<\/p>\n<p>\n  a<sub>12<\/sub> = 14 + (12 \u2212 1) &middot; 7 = 14 + 11 &middot; 7 = 14 + 77 = 91\n<\/p>\n<p>\n  Dwunastym wyrazem ci\u0105gu jest wi\u0119c liczba <strong>91<\/strong>, czyli odpowied\u017a <strong>c)<\/strong>.\n<\/p>\n\n        <\/div>\n    <\/div>\n    \n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>zadanie 14 \u2013 sierpie\u0144 2015 (1pkt) Wszystkie dwucyfrowe liczby naturalne podzielne przez 7 tworz\u0105 rosn\u0105cy ci\u0105g arytmetyczny. Dwunastym wyrazem tego ci\u0105gu jest liczba: a) 77 b) 84 c) 91 d) 98<\/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":[25,26,159,81,83],"tags":[],"class_list":["post-1171","post","type-post","status-publish","format-standard","hentry","category-ciag-arytmetyczny","category-obliczanie-wyrazow-ciagu","category-sierpien-2015","category-zadania-maturalne","category-zadania-tematami"],"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 2015 (1pkt) Wszystkie dwucyfrowe liczby naturalne podzielne przez 7 tworz\u0105 rosn\u0105cy ci\u0105g arytmetyczny. Dwunastym wyrazem tego ci\u0105gu jest liczba: a) 77 b) 84 c) 91 d) 98","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/mymatma.pl\/index.php?rest_route=\/wp\/v2\/posts\/1171","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=1171"}],"version-history":[{"count":1,"href":"https:\/\/mymatma.pl\/index.php?rest_route=\/wp\/v2\/posts\/1171\/revisions"}],"predecessor-version":[{"id":1172,"href":"https:\/\/mymatma.pl\/index.php?rest_route=\/wp\/v2\/posts\/1171\/revisions\/1172"}],"wp:attachment":[{"href":"https:\/\/mymatma.pl\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1171"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mymatma.pl\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1171"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mymatma.pl\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1171"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}