{"id":1131,"date":"2025-12-18T12:15:07","date_gmt":"2025-12-18T11:15:07","guid":{"rendered":"http:\/\/mymatma.pl\/?p=1131"},"modified":"2025-12-18T12:35:57","modified_gmt":"2025-12-18T11:35:57","slug":"zadanie-83","status":"publish","type":"post","link":"https:\/\/mymatma.pl\/?p=1131","title":{"rendered":"Zadanie 83"},"content":{"rendered":"\n<p><strong>zadanie 13 \u2013 czerwiec 2020 (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 . Czwarty wyraz tego ci\u0105gu jest r\u00f3wny a<sub>4<\/sub>=2020 . Suma a<sub>2<\/sub>+a<sub>6<\/sub> jest r\u00f3wna:<\/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) 505<\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<p>b) 1010<\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<p>c) 2020<\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<p>d) 4040<\/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_69e2285bf2a80\">\n        <button class=\"premium-btn-odp\"\n                data-id=\"odp_69e2285bf2a80\"\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>c) 2020<\/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_69e2285bf2a8a\">\n        <button class=\"premium-btn-wyjasnienie\"\n                data-id=\"wyjasnienie_69e2285bf2a8a\"\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>\nW zadaniu podano, \u017ce czwarty wyraz ci\u0105gu arytmetycznego jest r\u00f3wny:<br>\na\u2084 = 2020.\n<br><br>\nKorzystamy ze wzoru na n\u2011ty wyraz ci\u0105gu arytmetycznego:<br>\na\u2099 = a\u2081 + (n \u2212 1)r\n<br><br>\nWyrazy a\u2082 i a\u2086 mo\u017cna zapisa\u0107 jako:<br>\na\u2082 = a\u2081 + r<br>\na\u2086 = a\u2081 + 5r\n<br><br>\nDodajemy je:<br>\na\u2082 + a\u2086 = (a\u2081 + r) + (a\u2081 + 5r) = 2a\u2081 + 6r\n<br><br>\nZauwa\u017camy, \u017ce:<br>\na\u2084 = a\u2081 + 3r\n<br>\n2a\u2084 = 2(a\u2081 + 3r) = 2a\u2081 + 6r\n<br><br>\nZatem:<br>\na\u2082 + a\u2086 = 2a\u2084 = 2 \u00b7 2020 = 4040\n<br><br>\n<strong>Prawid\u0142owa odpowied\u017a: d) 4040<\/strong>\n<\/p>\n\n        <\/div>\n    <\/div>\n    \n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>zadanie 13 \u2013 czerwiec 2020 (1pkt) Ci\u0105g arytmetyczny (an) jest okre\u015blony dla ka\u017cdej liczby naturalnej n\u22651 . Czwarty wyraz tego ci\u0105gu jest r\u00f3wny a4=2020 . Suma a2+a6 jest r\u00f3wna: a) 505 b) 1010 c) 2020 d) 4040<\/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":[25,38,26,81,83],"tags":[23,37,24],"class_list":["post-1131","post","type-post","status-publish","format-standard","hentry","category-ciag-arytmetyczny","category-czerwiec-2020","category-obliczanie-wyrazow-ciagu","category-zadania-maturalne","category-zadania-tematami","tag-ciag-arytmetyczny","tag-czerwiec-2020","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 czerwiec 2020 (1pkt) Ci\u0105g arytmetyczny (an) jest okre\u015blony dla ka\u017cdej liczby naturalnej n\u22651 . Czwarty wyraz tego ci\u0105gu jest r\u00f3wny a4=2020 . Suma a2+a6 jest r\u00f3wna: a) 505 b) 1010 c) 2020 d) 4040","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/mymatma.pl\/index.php?rest_route=\/wp\/v2\/posts\/1131","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=1131"}],"version-history":[{"count":2,"href":"https:\/\/mymatma.pl\/index.php?rest_route=\/wp\/v2\/posts\/1131\/revisions"}],"predecessor-version":[{"id":1143,"href":"https:\/\/mymatma.pl\/index.php?rest_route=\/wp\/v2\/posts\/1131\/revisions\/1143"}],"wp:attachment":[{"href":"https:\/\/mymatma.pl\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1131"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mymatma.pl\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1131"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mymatma.pl\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1131"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}