{"id":878,"date":"2025-12-05T10:52:58","date_gmt":"2025-12-05T09:52:58","guid":{"rendered":"https:\/\/mymatma.pl\/?p=878"},"modified":"2025-12-05T11:14:49","modified_gmt":"2025-12-05T10:14:49","slug":"zadanie-26","status":"publish","type":"post","link":"https:\/\/mymatma.pl\/?p=878","title":{"rendered":"Zadanie 26"},"content":{"rendered":"\n<p><strong>zadanie 15 \u2013 sierpie\u0144 2010( 1 pkt)<\/strong><\/p>\n\n\n\n<p>W malej\u0105cym ci\u0105gu geometrycznym (a<sub>n<\/sub>) mamy: a<sub>1<\/sub>=\u22122 i a<sub>3<\/sub>=\u22124 . Iloraz 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<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\"><\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\"><\/div>\n<\/div>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\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\"><\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\"><\/div>\n<\/div>\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_69e22ae25970d\">\n        <button class=\"premium-btn-odp\"\n                data-id=\"odp_69e22ae25970d\"\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. \n        <\/div>\n    <\/div>\n    \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_69e22ae259718\">\n        <button class=\"premium-btn-wyjasnienie\"\n                data-id=\"wyjasnienie_69e22ae259718\"\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<div class=\"card\" role=\"article\" style=\"font-family:system-ui,-apple-system,Segoe UI,Roboto,'Helvetica Neue',Arial;line-height:1.5;color:#111;padding:18px;background:#fff;border:1px solid #e2e6ea;border-radius:10px;max-width:760px;margin:16px auto;box-shadow:0 6px 20px rgba(18,38,63,0.06)\">\n\n  <p>Dany jest malej\u0105cy ci\u0105g geometryczny <code>(a<sub>n<\/sub>)<\/code> z pierwszym wyrazem <strong>a\u2081 = \u22122<\/strong> i trzecim wyrazem <strong>a\u2083 = \u22124<\/strong>. Obliczamy iloraz <em>q<\/em>.<\/p>\n\n  <p><strong>Krok 1 \u2014 wz\u00f3r og\u00f3lny ci\u0105gu geometrycznego:<\/strong><\/p>\n  <p style=\"background:#fbfdff;padding:8px;border-radius:6px;border:1px solid #eef6ff;display:inline-block\">\n    a\u2083 = a\u2081\u00b7q\u00b2\n  <\/p>\n\n  <p><strong>Krok 2 \u2014 podstaw dane warto\u015bci:<\/strong><\/p>\n  <p style=\"background:#fbfdff;padding:8px;border-radius:6px;border:1px solid #eef6ff;display:inline-block\">\n    \u22124 = (\u22122)\u00b7q\u00b2\n  <\/p>\n\n  <p><strong>Krok 3 \u2014 podziel przez \u22122 i oblicz pierwiastek:<\/strong><\/p>\n  <p style=\"background:#fbfdff;padding:8px;border-radius:6px;border:1px solid #eef6ff;display:inline-block\">\n    q\u00b2 = (\u22124)\/(\u22122) = 2<br>\n    q = \u00b1\u221a2\n  <\/p>\n\n  <p><strong>Krok 4 \u2014 uwzgl\u0119dnij malej\u0105cy ci\u0105g:<\/strong><\/p>\n  <p>Malej\u0105cy ci\u0105g geometryczny z ujemnym wyrazem pocz\u0105tkowym oznacza, \u017ce iloraz <em>q<\/em> jest ujemny. Zatem:<\/p>\n\n  <div style=\"margin-top:14px;padding:12px;border-radius:8px;background:#f0faf0;border:1px solid #d8f1d8;color:#066a06;font-weight:600\">\n    Iloraz q = <strong>\u2212\u221a2<\/strong>\n  <\/div>\n\n  <div style=\"margin-top:14px\">\n    <span style=\"display:inline-block;padding:8px 10px;border-radius:6px;border:1px solid #1e90ff;background:#e9f4ff;font-weight:600\">a) -2<\/span>\n    <span style=\"display:inline-block;padding:8px 10px;border-radius:6px;border:1px solid #ddd;background:#fafafa\">b) 2<\/span>\n    <span style=\"display:inline-block;padding:8px 10px;border-radius:6px;border:1px solid #1e90ff;background:#e9f4ff;font-weight:600\">c) -\u221a2<\/span>\n    <span style=\"display:inline-block;padding:8px 10px;border-radius:6px;border:1px solid #ddd;background:#fafafa\">d) \u221a2<\/span>\n  <\/div>\n\n<\/div>\n\n        <\/div>\n    <\/div>\n    \n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>zadanie 15 \u2013 sierpie\u0144 2010( 1 pkt) W malej\u0105cym ci\u0105gu geometrycznym (an) mamy: a1=\u22122 i a3=\u22124 . Iloraz tego ci\u0105gu jest r\u00f3wny:<\/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":[31,49,80,81,83],"tags":[79],"class_list":["post-878","post","type-post","status-publish","format-standard","hentry","category-ciag-geometryczny","category-iloraz-ciagu","category-sierpien-2010","category-zadania-maturalne","category-zadania-tematami","tag-sierpien-2010"],"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 15 \u2013 sierpie\u0144 2010( 1 pkt) W malej\u0105cym ci\u0105gu geometrycznym (an) mamy: a1=\u22122 i a3=\u22124 . Iloraz tego ci\u0105gu jest r\u00f3wny:","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/mymatma.pl\/index.php?rest_route=\/wp\/v2\/posts\/878","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=878"}],"version-history":[{"count":1,"href":"https:\/\/mymatma.pl\/index.php?rest_route=\/wp\/v2\/posts\/878\/revisions"}],"predecessor-version":[{"id":879,"href":"https:\/\/mymatma.pl\/index.php?rest_route=\/wp\/v2\/posts\/878\/revisions\/879"}],"wp:attachment":[{"href":"https:\/\/mymatma.pl\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=878"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mymatma.pl\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=878"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mymatma.pl\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=878"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}