{"id":715,"date":"2025-12-04T08:38:02","date_gmt":"2025-12-04T07:38:02","guid":{"rendered":"http:\/\/mymatma.pl\/?p=715"},"modified":"2025-12-05T11:38:39","modified_gmt":"2025-12-05T10:38:39","slug":"zadanie-6","status":"publish","type":"post","link":"https:\/\/mymatma.pl\/?p=715","title":{"rendered":"Zadanie 6"},"content":{"rendered":"\n<p><br><strong>zadanie 21 grudzie\u0144 2013 (1pkt)<\/strong><\/p>\n\n\n\n<p><br>W dziewi\u0119ciowyrazowym ci\u0105gu geometrycznym o wyrazach dodatnich pierwszy wyraz jest r\u00f3wny 3, a ostatni wyraz jest r\u00f3wny 12. Pi\u0105ty wyraz 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_69e22acebf2da\">\n        <button class=\"premium-btn-odp\"\n                data-id=\"odp_69e22acebf2da\"\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 B.\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_69e22acebf2e5\">\n        <button class=\"premium-btn-wyjasnienie\"\n                data-id=\"wyjasnienie_69e22acebf2e5\"\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>\n  <p>Mamy ci\u0105g geometryczny <code>(a\u2099)<\/code> o 9 wyrazach, z <code>a\u2081 = 3<\/code> i <code>a\u2089 = 12<\/code>. Chcemy znale\u017a\u0107 pi\u0105ty wyraz <code>a\u2085<\/code>.<\/p>\n\n  <p>Dla ci\u0105gu geometrycznego o ilorazie <code>q<\/code>:<\/p>\n  <p><code>a\u2099 = a\u2081 \u00b7 q^(n\u22121)<\/code><\/p>\n\n  <p>Skoro <code>a\u2089 = a\u2081\u00b7q\u2078<\/code>, mamy:<\/p>\n  <p><code>12 = 3\u00b7q\u2078<\/code><\/p>\n  <p><code>q\u2078 = 12 \/ 3 = 4<\/code><\/p>\n  <p><code>q = 4^(1\/8) = \u221a2^(1\/2) \u2248 1.1892<\/code><\/p>\n\n  <p>Teraz obliczamy <code>a\u2085 = a\u2081\u00b7q\u2074<\/code>:<\/p>\n  <p><code>a\u2085 = 3 \u00b7 q\u2074 = 3 \u00b7 (q\u2078)^(1\/2) = 3 \u00b7 \u221a4 = 3 \u00b7 2 = 6<\/code><\/p>\n\n  <p><strong>Poprawna odpowied\u017a: b) 6<\/strong><\/p>\n<\/div>\n        <\/div>\n    <\/div>\n    \n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>zadanie 21 grudzie\u0144 2013 (1pkt) W dziewi\u0119ciowyrazowym ci\u0105gu geometrycznym o wyrazach dodatnich pierwszy wyraz jest r\u00f3wny 3, a ostatni wyraz jest r\u00f3wny 12. Pi\u0105ty wyraz 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":[31,40,32,81,83],"tags":[29,39,28],"class_list":["post-715","post","type-post","status-publish","format-standard","hentry","category-ciag-geometryczny","category-grudzien-2013","category-obliczanie-wyrazow-ciagu-geometrycznego","category-zadania-maturalne","category-zadania-tematami","tag-ciag-geometryczny","tag-grudzien-2013","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 21 grudzie\u0144 2013 (1pkt) W dziewi\u0119ciowyrazowym ci\u0105gu geometrycznym o wyrazach dodatnich pierwszy wyraz jest r\u00f3wny 3, a ostatni wyraz jest r\u00f3wny 12. Pi\u0105ty wyraz tego ci\u0105gu jest r\u00f3wny:","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/mymatma.pl\/index.php?rest_route=\/wp\/v2\/posts\/715","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=715"}],"version-history":[{"count":1,"href":"https:\/\/mymatma.pl\/index.php?rest_route=\/wp\/v2\/posts\/715\/revisions"}],"predecessor-version":[{"id":716,"href":"https:\/\/mymatma.pl\/index.php?rest_route=\/wp\/v2\/posts\/715\/revisions\/716"}],"wp:attachment":[{"href":"https:\/\/mymatma.pl\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=715"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mymatma.pl\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=715"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mymatma.pl\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=715"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}