Rozwi\u0105zanie ci\u0105gu geometrycznego<\/title>\n<\/head>\nMamy dane: ci\u0105g geometryczny (an<\/sub>), n \u2265 1, taki \u017ce:<\/p>\n<ul>\n <li>a2<\/sub> = 1\/6<\/li>\n <li>a3<\/sub> = 1\/9<\/li>\n<\/ul>\n\nChcemy znale\u017a\u0107 a5<\/sub>.<\/p>\n\n<ol>\n <li>Wyra\u017cenie og\u00f3lne ci\u0105gu geometrycznego:<\/strong> \n an<\/sub> = a1<\/sub> * q^(n-1), gdzie a1<\/sub> to pierwszy wyraz, a q to iloraz ci\u0105gu.<\/li>\n\n <li>Zapisanie danych wyraz\u00f3w:<\/strong> \n a2<\/sub> = a1<\/sub> * q = 1\/6 \n a3<\/sub> = a1<\/sub> * q\u00b2 = 1\/9<\/li>\n\n <li>Wyznaczenie ilorazu q:<\/strong> \n q = a3<\/sub> \/ a2<\/sub> = (1\/9) \/ (1\/6) = 6\/9 = 2\/3<\/li>\n\n <li>Wyznaczenie a1<\/sub>:<\/strong> \n a1<\/sub> = a2<\/sub> \/ q = (1\/6) \/ (2\/3) = 1\/4<\/li>\n\n <li>Obliczenie a5<\/sub>:<\/strong> \n a5<\/sub> = a1<\/sub> * q\u2074 = (1\/4) * (2\/3)\u2074 = (1\/4) * (16\/81) = 16\/324 = 4\/81<\/li>\n<\/ol>\n\nOdpowied\u017a:<\/strong> 4\/81 (opcja c)<\/p>\n\n<\/body>\n<\/html>\n\n <\/div>\n <\/div>\n \n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"","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":[31,33,32,81,83],"tags":[29,30,28],"class_list":["post-670","post","type-post","status-publish","format-standard","hentry","category-ciag-geometryczny","category-grudzien-2024","category-obliczanie-wyrazow-ciagu-geometrycznego","category-zadania-maturalne","category-zadania-tematami","tag-ciag-geometryczny","tag-grudzien-2024","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":null,"jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/mymatma.pl\/index.php?rest_route=\/wp\/v2\/posts\/670","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=670"}],"version-history":[{"count":9,"href":"https:\/\/mymatma.pl\/index.php?rest_route=\/wp\/v2\/posts\/670\/revisions"}],"predecessor-version":[{"id":824,"href":"https:\/\/mymatma.pl\/index.php?rest_route=\/wp\/v2\/posts\/670\/revisions\/824"}],"wp:attachment":[{"href":"https:\/\/mymatma.pl\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=670"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mymatma.pl\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=670"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mymatma.pl\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=670"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}

\n \n\n\n\n\nRozwi\u0105zanie ci\u0105gu geometrycznego<\/title>\n<\/head>\nMamy dane: ci\u0105g geometryczny (an<\/sub>), n \u2265 1, taki \u017ce:<\/p>\n<ul>\n <li>a2<\/sub> = 1\/6<\/li>\n <li>a3<\/sub> = 1\/9<\/li>\n<\/ul>\n\nChcemy znale\u017a\u0107 a5<\/sub>.<\/p>\n\n<ol>\n <li>Wyra\u017cenie og\u00f3lne ci\u0105gu geometrycznego:<\/strong> \n an<\/sub> = a1<\/sub> * q^(n-1), gdzie a1<\/sub> to pierwszy wyraz, a q to iloraz ci\u0105gu.<\/li>\n\n <li>Zapisanie danych wyraz\u00f3w:<\/strong> \n a2<\/sub> = a1<\/sub> * q = 1\/6 \n a3<\/sub> = a1<\/sub> * q\u00b2 = 1\/9<\/li>\n\n <li>Wyznaczenie ilorazu q:<\/strong> \n q = a3<\/sub> \/ a2<\/sub> = (1\/9) \/ (1\/6) = 6\/9 = 2\/3<\/li>\n\n <li>Wyznaczenie a1<\/sub>:<\/strong> \n a1<\/sub> = a2<\/sub> \/ q = (1\/6) \/ (2\/3) = 1\/4<\/li>\n\n <li>Obliczenie a5<\/sub>:<\/strong> \n a5<\/sub> = a1<\/sub> * q\u2074 = (1\/4) * (2\/3)\u2074 = (1\/4) * (16\/81) = 16\/324 = 4\/81<\/li>\n<\/ol>\n\nOdpowied\u017a:<\/strong> 4\/81 (opcja c)<\/p>\n\n<\/body>\n<\/html>\n\n <\/div>\n <\/div>\n \n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"","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":[31,33,32,81,83],"tags":[29,30,28],"class_list":["post-670","post","type-post","status-publish","format-standard","hentry","category-ciag-geometryczny","category-grudzien-2024","category-obliczanie-wyrazow-ciagu-geometrycznego","category-zadania-maturalne","category-zadania-tematami","tag-ciag-geometryczny","tag-grudzien-2024","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":null,"jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/mymatma.pl\/index.php?rest_route=\/wp\/v2\/posts\/670","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=670"}],"version-history":[{"count":9,"href":"https:\/\/mymatma.pl\/index.php?rest_route=\/wp\/v2\/posts\/670\/revisions"}],"predecessor-version":[{"id":824,"href":"https:\/\/mymatma.pl\/index.php?rest_route=\/wp\/v2\/posts\/670\/revisions\/824"}],"wp:attachment":[{"href":"https:\/\/mymatma.pl\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=670"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mymatma.pl\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=670"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mymatma.pl\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=670"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}