{"id":1129,"date":"2025-12-18T12:09:40","date_gmt":"2025-12-18T11:09:40","guid":{"rendered":"http:\/\/mymatma.pl\/?p=1129"},"modified":"2025-12-18T12:36:29","modified_gmt":"2025-12-18T11:36:29","slug":"zadanie-82","status":"publish","type":"post","link":"https:\/\/mymatma.pl\/?p=1129","title":{"rendered":"Zadanie 82"},"content":{"rendered":"\n<p><strong>zadanie 12 \u2013 marzec 2021 (1 pkt)<\/strong><\/p>\n\n\n\n<p>Ci\u0105g (a<sub>n<\/sub>) , okre\u015blony dla ka\u017cdej liczby naturalnej n\u22651 , jest arytmetyczny. R\u00f3\u017cnica tego ci\u0105gu jest r\u00f3wna 5 , a pierwszy wyraz tego ci\u0105gu jest r\u00f3wny (\u22123) . Wtedy iloraz (a<sub>4<\/sub>)\/(a<sub>2<\/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) 5\/3<\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<p>b) 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) 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) 25<\/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_69e227a759a1a\">\n        <button class=\"premium-btn-odp\"\n                data-id=\"odp_69e227a759a1a\"\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) 2<\/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_69e227a759a25\">\n        <button class=\"premium-btn-wyjasnienie\"\n                data-id=\"wyjasnienie_69e227a759a25\"\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>\nDany jest ci\u0105g arytmetyczny o pierwszym wyrazie <strong>a\u2081 = -3<\/strong> oraz r\u00f3\u017cnicy <strong>r = 5<\/strong>.  \nAby obliczy\u0107 iloraz <strong>a\u2084 \/ a\u2082<\/strong>, najpierw wyznaczamy te wyrazy.\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>\nObliczamy a\u2082:<br>\na\u2082 = -3 + 1\u00b75 = 2\n<br><br>\nObliczamy a\u2084:<br>\na\u2084 = -3 + 3\u00b75 = -3 + 15 = 12\n<br><br>\nTeraz liczymy iloraz:<br>\na\u2084 \/ a\u2082 = 12 \/ 2 = 2\n<br><br>\n<strong>Prawid\u0142owa odpowied\u017a: b) 2<\/strong>\n<\/p>\n\n        <\/div>\n    <\/div>\n    \n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>zadanie 12 \u2013 marzec 2021 (1 pkt) Ci\u0105g (an) , okre\u015blony dla ka\u017cdej liczby naturalnej n\u22651 , jest arytmetyczny. R\u00f3\u017cnica tego ci\u0105gu jest r\u00f3wna 5 , a pierwszy wyraz tego ci\u0105gu jest r\u00f3wny (\u22123) . Wtedy iloraz (a4)\/(a2) jest r\u00f3wny: a) 5\/3 b) 2 c) 6 d) 25<\/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":[25,94,26,81,83],"tags":[23,92,24],"class_list":["post-1129","post","type-post","status-publish","format-standard","hentry","category-ciag-arytmetyczny","category-marzec-2021","category-obliczanie-wyrazow-ciagu","category-zadania-maturalne","category-zadania-tematami","tag-ciag-arytmetyczny","tag-marzec-2021","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 12 \u2013 marzec 2021 (1 pkt) Ci\u0105g (an) , okre\u015blony dla ka\u017cdej liczby naturalnej n\u22651 , jest arytmetyczny. R\u00f3\u017cnica tego ci\u0105gu jest r\u00f3wna 5 , a pierwszy wyraz tego ci\u0105gu jest r\u00f3wny (\u22123) . Wtedy iloraz (a4)\/(a2) jest r\u00f3wny: a) 5\/3 b) 2 c) 6 d) 25","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/mymatma.pl\/index.php?rest_route=\/wp\/v2\/posts\/1129","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=1129"}],"version-history":[{"count":2,"href":"https:\/\/mymatma.pl\/index.php?rest_route=\/wp\/v2\/posts\/1129\/revisions"}],"predecessor-version":[{"id":1144,"href":"https:\/\/mymatma.pl\/index.php?rest_route=\/wp\/v2\/posts\/1129\/revisions\/1144"}],"wp:attachment":[{"href":"https:\/\/mymatma.pl\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1129"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mymatma.pl\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1129"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mymatma.pl\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1129"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}