{"id":1185,"date":"2025-12-19T07:59:17","date_gmt":"2025-12-19T06:59:17","guid":{"rendered":"https:\/\/mymatma.pl\/?p=1185"},"modified":"2025-12-19T07:59:20","modified_gmt":"2025-12-19T06:59:20","slug":"zadanie-96","status":"publish","type":"post","link":"https:\/\/mymatma.pl\/?p=1185","title":{"rendered":"Zadanie 96"},"content":{"rendered":"\n<p><strong>zadanie 11 \u2013 maj 2010 (1pkt)<\/strong><\/p>\n\n\n\n<p>W ci\u0105gu arytmetycznym (a<sub>n<\/sub>) dane s\u0105: a<sub>3<\/sub>=13 i a<sub>5<\/sub>=39 . Wtedy wyraz a<sub>1<\/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) 13<\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<p>b) 0<\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<p>c) -13<\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<p>d) -26<\/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_69e22b4d8c127\">\n        <button class=\"premium-btn-odp\"\n                data-id=\"odp_69e22b4d8c127\"\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) -13.\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_69e22b4d8c138\">\n        <button class=\"premium-btn-wyjasnienie\"\n                data-id=\"wyjasnienie_69e22b4d8c138\"\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 mo\u017cna obliczy\u0107 ze wzoru: \n<strong>a<sub>n<\/sub> = a<sub>1<\/sub> + (n-1)\u00b7d<\/strong>, gdzie <em>d<\/em> to r\u00f3\u017cnica ci\u0105gu.<\/p>\n\n<p>Dane s\u0105:<\/p>\n<ul>\n  <li>a<sub>3<\/sub> = 13<\/li>\n  <li>a<sub>5<\/sub> = 39<\/li>\n<\/ul>\n\n<p>Podstawiamy do wzoru:<\/p>\n<ul>\n  <li>a<sub>3<\/sub> = a<sub>1<\/sub> + 2d = 13<\/li>\n  <li>a<sub>5<\/sub> = a<sub>1<\/sub> + 4d = 39<\/li>\n<\/ul>\n\n<p>Odejmujemy r\u00f3wnania:<\/p>\n<p>(a<sub>1<\/sub> + 4d) \u2013 (a<sub>1<\/sub> + 2d) = 39 \u2013 13<\/p>\n<p>2d = 26 \u21d2 d = 13<\/p>\n\n<p>Teraz obliczamy a<sub>1<\/sub>:<\/p>\n<p>a<sub>3<\/sub> = a<sub>1<\/sub> + 2d = 13<\/p>\n<p>a<sub>1<\/sub> = 13 \u2013 2\u00b713 = 13 \u2013 26 = <strong>-13<\/strong><\/p>\n\n<h3>Odpowied\u017a: c) -13<\/h3>\n\n        <\/div>\n    <\/div>\n    \n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>zadanie 11 \u2013 maj 2010 (1pkt) W ci\u0105gu arytmetycznym (an) dane s\u0105: a3=13 i a5=39 . Wtedy wyraz a1 jest r\u00f3wny: a) 13 b) 0 c) -13 d) -26<\/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":[25,86,26,81,83],"tags":[23,85,24],"class_list":["post-1185","post","type-post","status-publish","format-standard","hentry","category-ciag-arytmetyczny","category-maj-2010","category-obliczanie-wyrazow-ciagu","category-zadania-maturalne","category-zadania-tematami","tag-ciag-arytmetyczny","tag-maj-2010","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 11 \u2013 maj 2010 (1pkt) W ci\u0105gu arytmetycznym (an) dane s\u0105: a3=13 i a5=39 . Wtedy wyraz a1 jest r\u00f3wny: a) 13 b) 0 c) -13 d) -26","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/mymatma.pl\/index.php?rest_route=\/wp\/v2\/posts\/1185","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=1185"}],"version-history":[{"count":1,"href":"https:\/\/mymatma.pl\/index.php?rest_route=\/wp\/v2\/posts\/1185\/revisions"}],"predecessor-version":[{"id":1186,"href":"https:\/\/mymatma.pl\/index.php?rest_route=\/wp\/v2\/posts\/1185\/revisions\/1186"}],"wp:attachment":[{"href":"https:\/\/mymatma.pl\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1185"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mymatma.pl\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1185"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mymatma.pl\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1185"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}