{"id":1617,"date":"2025-12-31T13:54:28","date_gmt":"2025-12-31T12:54:28","guid":{"rendered":"http:\/\/mymatma.pl\/?p=1617"},"modified":"2025-12-31T14:48:26","modified_gmt":"2025-12-31T13:48:26","slug":"zadanie-156","status":"publish","type":"post","link":"https:\/\/mymatma.pl\/?p=1617","title":{"rendered":"Zadanie 156"},"content":{"rendered":"\n<p><strong>zadanie 99 &#8211; zbi\u00f3r zada\u0144 CKE (zadanie otwarte) <\/strong><\/p>\n\n\n\n<p>Liczby a, b, c tworz\u0105 w podanej kolejno\u015bci ci\u0105g geometryczny. Suma tych liczb jest r\u00f3wna 93.<br>Te same liczby, w podanej kolejno\u015bci s\u0105 pierwszym, drugim i si\u00f3dmym wyrazem ci\u0105gu<br>arytmetycznego. Oblicz a, b i c.<\/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_69e23d89a314e\">\n        <button class=\"premium-btn-odp\"\n                data-id=\"odp_69e23d89a314e\"\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:<ul> <li><strong>a = 3<\/strong><\/li> <li><strong>b = 15<\/strong><\/li> <li><strong>c = 75<\/strong><\/li> <\/ul>\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_69e23d89a315d\">\n        <button class=\"premium-btn-wyjasnienie\"\n                data-id=\"wyjasnienie_69e23d89a315d\"\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<h2>Wyja\u015bnienie<\/h2\n\n<h3>Krok 1: Sprawdzenie ci\u0105gu geometrycznego<\/h3>\n\n<p>Obliczamy iloraz:<\/p>\n\n<p><code>b \/ a = 15 \/ 3 = 5<\/code><\/p>\n<p><code>c \/ b = 75 \/ 15 = 5<\/code><\/p>\n\n<p>Iloraz jest sta\u0142y i r\u00f3wny 5, wi\u0119c liczby tworz\u0105 ci\u0105g geometryczny.<\/p>\n\n<h3>Krok 2: Sprawdzenie ci\u0105gu arytmetycznego<\/h3>\n\n<p>Liczby <code>a<\/code>, <code>b<\/code>, <code>c<\/code> s\u0105 odpowiednio pierwszym, drugim i si\u00f3dmym wyrazem ci\u0105gu arytmetycznego.<\/p>\n\n<p>R\u00f3\u017cnica ci\u0105gu:<\/p>\n\n<p><code>d = b \u2212 a = 15 \u2212 3 = 12<\/code><\/p>\n\n<p>Si\u00f3dmy wyraz ci\u0105gu arytmetycznego ma posta\u0107:<\/p>\n\n<p><code>a\u2087 = a + 6d = 3 + 6\u00b712 = 3 + 72 = 75<\/code><\/p>\n\n<p>Otrzymujemy dok\u0142adnie warto\u015b\u0107 <code>c<\/code>, wi\u0119c warunek jest spe\u0142niony.<\/p>\n\n<h3>Krok 3: Sprawdzenie sumy<\/h3>\n\n<p><code>a + b + c = 3 + 15 + 75 = 93<\/code><\/p>\n\n<p>Suma zgadza si\u0119 z tre\u015bci\u0105 zadania.<\/p>\n\n<h3>Wniosek<\/h3>\n\n<p>Liczby <strong>3, 15, 75<\/strong> spe\u0142niaj\u0105 wszystkie warunki zadania: tworz\u0105 ci\u0105g geometryczny, s\u0105 odpowiednio pierwszym, drugim i si\u00f3dmym wyrazem ci\u0105gu arytmetycznego oraz ich suma wynosi 93.<\/p>\n\n        <\/div>\n    <\/div>\n    \n<\/div>\n<\/div>\n\n\n\n<p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>zadanie 99 &#8211; zbi\u00f3r zada\u0144 CKE (zadanie otwarte) Liczby a, b, c tworz\u0105 w podanej kolejno\u015bci ci\u0105g geometryczny. Suma tych liczb jest r\u00f3wna 93.Te same liczby, w podanej kolejno\u015bci s\u0105 pierwszym, drugim i si\u00f3dmym wyrazem ci\u0105guarytmetycznego. Oblicz a, b i c.<\/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":[105,31,81,83,146],"tags":[144,29,145],"class_list":["post-1617","post","type-post","status-publish","format-standard","hentry","category-ciag-arytmetyczny-i-geometryczny","category-ciag-geometryczny","category-zadania-maturalne","category-zadania-tematami","category-zbior-zadan-cke","tag-ciag-arytmetyczny-i-geometryczny","tag-ciag-geometryczny","tag-zbior-zadan-cke"],"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 99 &#8211; zbi\u00f3r zada\u0144 CKE (zadanie otwarte) Liczby a, b, c tworz\u0105 w podanej kolejno\u015bci ci\u0105g geometryczny. Suma tych liczb jest r\u00f3wna 93.Te same liczby, w podanej kolejno\u015bci s\u0105 pierwszym, drugim i si\u00f3dmym wyrazem ci\u0105guarytmetycznego. Oblicz a, b i c.","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/mymatma.pl\/index.php?rest_route=\/wp\/v2\/posts\/1617","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=1617"}],"version-history":[{"count":1,"href":"https:\/\/mymatma.pl\/index.php?rest_route=\/wp\/v2\/posts\/1617\/revisions"}],"predecessor-version":[{"id":1623,"href":"https:\/\/mymatma.pl\/index.php?rest_route=\/wp\/v2\/posts\/1617\/revisions\/1623"}],"wp:attachment":[{"href":"https:\/\/mymatma.pl\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1617"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mymatma.pl\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1617"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mymatma.pl\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1617"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}