{"id":697,"date":"2025-12-03T14:26:39","date_gmt":"2025-12-03T13:26:39","guid":{"rendered":"https:\/\/mymatma.pl\/?p=697"},"modified":"2025-12-05T11:39:12","modified_gmt":"2025-12-05T10:39:12","slug":"zadanie-3","status":"publish","type":"post","link":"https:\/\/mymatma.pl\/?p=697","title":{"rendered":"Zadanie 3"},"content":{"rendered":"\n<p><strong>zadanie 17 \u2013 sierpie\u0144 2023 (1pkt)<\/strong><\/p>\n\n\n\n<p>Dany jest ci\u0105g geometryczny (a<sub>n<\/sub>) , okre\u015blony dla ka\u017cdej liczby naturalnej n\u22651 . Pierwszy wyraz tego ci\u0105gu jest r\u00f3wny 128 , natomiast iloraz ci\u0105gu jest r\u00f3wny (\u22121\/2) .<\/p>\n\n\n\n<p>Oce\u0144 prawdziwo\u015b\u0107 poni\u017cszych stwierdze\u0144. Wybierz P, je\u015bli stwierdzenie jest prawdziwe, albo F \u2013 je\u015bli jest fa\u0142szywe.<br>&#8211; Wyraz a<sub>2023<\/sub> jest liczb\u0105 ujemn\u0105. P\/F<br>&#8211; R\u00f3\u017cnica a<sub>3<\/sub>\u2212a<sub>2 <\/sub>jest r\u00f3wna 96 .P\/F<\/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=\"premium-wrapper-odp\" id=\"odp_69e22a274f815\">\n        <button class=\"premium-btn-odp\"\n                data-id=\"odp_69e22a274f815\"\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 FP.\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_69e22a274f81f\">\n        <button class=\"premium-btn-wyjasnienie\"\n                data-id=\"wyjasnienie_69e22a274f81f\"\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<!DOCTYPE html>\n<html lang=\"pl\">\n<head>\n<meta charset=\"UTF-8\">\n<title>Rozwi\u0105zanie zadania<\/title>\n<\/head>\n<body>\n\n<p>Dany ci\u0105g geometryczny: a\u2081 = 128, q = -1\/2<\/p>\n\n<ul>\n  <li><strong>Wyraz a<sub>2023<\/sub> jest liczb\u0105 ujemn\u0105:<\/strong> <strong>F<\/strong><br>\n  Wyja\u015bnienie: a<sub>2023<\/sub> = 128\u00b7(-1\/2)<sup>2022<\/sup> = 128\u00b7(1\/2)<sup>2022<\/sup> > 0, wi\u0119c wyraz jest dodatni.<\/li>\n\n  <li><strong>R\u00f3\u017cnica a\u2083 \u2212 a\u2082 jest r\u00f3wna 96:<\/strong> <strong>P<\/strong><br>\n  Wyja\u015bnienie: a\u2082 = -64, a\u2083 = 32, wi\u0119c a\u2083 \u2212 a\u2082 = 32 &#8211; (-64) = 96.<\/li>\n<\/ul>\n<\/body>\n<\/html>\n\n        <\/div>\n    <\/div>\n    \n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>zadanie 17 \u2013 sierpie\u0144 2023 (1pkt) Dany jest ci\u0105g geometryczny (an) , okre\u015blony dla ka\u017cdej liczby naturalnej n\u22651 . Pierwszy wyraz tego ci\u0105gu jest r\u00f3wny 128 , natomiast iloraz ci\u0105gu jest r\u00f3wny (\u22121\/2) . Oce\u0144 prawdziwo\u015b\u0107 poni\u017cszych stwierdze\u0144. Wybierz P, je\u015bli stwierdzenie jest prawdziwe, albo F \u2013 je\u015bli jest fa\u0142szywe.&#8211; Wyraz a2023 jest liczb\u0105 ujemn\u0105. [&hellip;]<\/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":[31,32,34,81,83],"tags":[29,28],"class_list":["post-697","post","type-post","status-publish","format-standard","hentry","category-ciag-geometryczny","category-obliczanie-wyrazow-ciagu-geometrycznego","category-sierpien-2023","category-zadania-maturalne","category-zadania-tematami","tag-ciag-geometryczny","tag-obliczanie-wyrazow-ciagu-geometrycznego"],"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 17 \u2013 sierpie\u0144 2023 (1pkt) Dany jest ci\u0105g geometryczny (an) , okre\u015blony dla ka\u017cdej liczby naturalnej n\u22651 . Pierwszy wyraz tego ci\u0105gu jest r\u00f3wny 128 , natomiast iloraz ci\u0105gu jest r\u00f3wny (\u22121\/2) . Oce\u0144 prawdziwo\u015b\u0107 poni\u017cszych stwierdze\u0144. Wybierz P, je\u015bli stwierdzenie jest prawdziwe, albo F \u2013 je\u015bli jest fa\u0142szywe.&#8211; Wyraz a2023 jest liczb\u0105 ujemn\u0105.&hellip;","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/mymatma.pl\/index.php?rest_route=\/wp\/v2\/posts\/697","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=697"}],"version-history":[{"count":3,"href":"https:\/\/mymatma.pl\/index.php?rest_route=\/wp\/v2\/posts\/697\/revisions"}],"predecessor-version":[{"id":825,"href":"https:\/\/mymatma.pl\/index.php?rest_route=\/wp\/v2\/posts\/697\/revisions\/825"}],"wp:attachment":[{"href":"https:\/\/mymatma.pl\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=697"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mymatma.pl\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=697"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mymatma.pl\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=697"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}