{"id":1665,"date":"2026-01-02T08:13:02","date_gmt":"2026-01-02T07:13:02","guid":{"rendered":"http:\/\/mymatma.pl\/?p=1665"},"modified":"2026-01-02T08:44:52","modified_gmt":"2026-01-02T07:44:52","slug":"zadanie-1-2","status":"publish","type":"post","link":"https:\/\/mymatma.pl\/?p=1665","title":{"rendered":"Zadanie 1"},"content":{"rendered":"\n<p><strong>Dany jest ci\u0105g geometryczny<\/strong><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mo stretchy=\"false\">(<\/mo><msub><mi>a<\/mi><mi>n<\/mi><\/msub><mo stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">(a_n)<\/annotation><\/semantics><\/math>.<br>Wyznacz <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msub><mi>a<\/mi><mn>1<\/mn><\/msub><\/mrow><annotation encoding=\"application\/x-tex\">a_1<\/annotation><\/semantics><\/math>\u200b, <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>q<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">q<\/annotation><\/semantics><\/math> oraz <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msub><mi>a<\/mi><mn>5<\/mn><\/msub><\/mrow><annotation encoding=\"application\/x-tex\">a_5<\/annotation><\/semantics><\/math>\u200b.<\/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<\/div>\n<\/div>\n\n\n\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\">\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_69e22ae2f1e35\">\n        <button class=\"premium-btn-odp\"\n                data-id=\"odp_69e22ae2f1e35\"\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            \nOdpowied\u017a to: a1\u200b=2,q=2,a5\u200b=32\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_69e22ae2f1e45\">\n        <button class=\"premium-btn-wyjasnienie\"\n                data-id=\"wyjasnienie_69e22ae2f1e45\"\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<p><strong>a)<\/strong> 2, 4, 8, 16, \u2026<\/p>\n\n<p>\na<sub>1<\/sub> = 2 \u2013 pierwszy wyraz ci\u0105gu<br>\na<sub>2<\/sub> = 4 \u2013 drugi wyraz ci\u0105gu<br>\na<sub>3<\/sub> = 8 \u2013 trzeci wyraz ci\u0105gu\n<\/p>\n\n<p>\nIloraz ci\u0105gu geometrycznego obliczamy, dziel\u0105c dwa kolejne wyrazy ci\u0105gu:\n<\/p>\n\n<p>\nq = a<sub>2<\/sub> \/ a<sub>1<\/sub> = 4 \/ 2 = 2\n<\/p>\n\n<p>\nIloraz mo\u017cna r\u00f3wnie\u017c obliczy\u0107 z innych kolejnych wyraz\u00f3w, np.:<br>\nq = a<sub>4<\/sub> \/ a<sub>3<\/sub>\n<\/p>\n\n<p>\nOstatecznie:<br>\nq = 2\n<\/p>\n\n<p><strong>Obliczamy wyraz a<sub>5<\/sub><\/strong><\/p>\n\n<p>\nDowolny wyraz ci\u0105gu geometrycznego mo\u017cemy obliczy\u0107 ze wzoru og\u00f3lnego:\n<\/p>\n\n<p>\na<sub>n<\/sub> = a<sub>1<\/sub> \u00b7 q<sup>n\u22121<\/sup>\n<\/p>\n\n        <\/div>\n    <\/div>\n    \n<\/div>\n<\/div>\n\n\n\n\n\n<p><strong>c)<\/strong> -125, 25, -5 , \u2026<\/p>\n\n\n\n<p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Dany jest ci\u0105g geometryczny(an)(a_n).Wyznacz a1a_1\u200b, qq oraz a5a_5\u200b. c) -125, 25, -5 , \u2026<\/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":[270,271],"tags":[273,272],"class_list":["post-1665","post","type-post","status-publish","format-standard","hentry","category-z-d-ciagi-geometryczne","category-z-d-okreslenie-ciagu-geometrycznego","tag-z-d-ciag-geometryczny","tag-z-d-okreslenie-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":"Dany jest ci\u0105g geometryczny(an)(a_n).Wyznacz a1a_1\u200b, qq oraz a5a_5\u200b. c) -125, 25, -5 , \u2026","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/mymatma.pl\/index.php?rest_route=\/wp\/v2\/posts\/1665","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=1665"}],"version-history":[{"count":3,"href":"https:\/\/mymatma.pl\/index.php?rest_route=\/wp\/v2\/posts\/1665\/revisions"}],"predecessor-version":[{"id":1675,"href":"https:\/\/mymatma.pl\/index.php?rest_route=\/wp\/v2\/posts\/1665\/revisions\/1675"}],"wp:attachment":[{"href":"https:\/\/mymatma.pl\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1665"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mymatma.pl\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1665"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mymatma.pl\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1665"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}