{"id":773,"date":"2025-12-04T12:10:04","date_gmt":"2025-12-04T11:10:04","guid":{"rendered":"http:\/\/mymatma.pl\/?p=773"},"modified":"2025-12-04T12:38:52","modified_gmt":"2025-12-04T11:38:52","slug":"zadanie-1","status":"publish","type":"post","link":"https:\/\/mymatma.pl\/?p=773","title":{"rendered":"Zadanie 1"},"content":{"rendered":"\n<p><p>Oblicz wyrazy a<sub>1<\/sub>, a<sub>3<\/sub>, a<sub>11<\/sub> ci\u0105gu geometrycznego okre\u015blonego wzorem og\u00f3lnym:<\/p><br><p>a) a<sub>n<\/sub> = 3\u00b7(1\/2)<sup>n<\/sup><br><br>b) a<sub>n<\/sub> = -1\/2\u00b73<sup>n<\/sup><br><br>c) a<sub>n<\/sub> = -1024\u00b7(-1\/4)<sup>n-1<\/sup><\/p><\/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_69e22a64c9c3f\">\n        <button class=\"premium-btn-odp\"\n                data-id=\"odp_69e22a64c9c3f\"\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            \na) a\u2081 = 3\/2, a\u2083 = 3\/8, a\u2081\u2081 = 3\/1024<br>\nb) a\u2081 = -3\/2, a\u2083 = -27\/2, a\u2081\u2081 = -177147\/2 <br>\nc) a\u2081 = -1024, a\u2083 = -256, a\u2081\u2081 = -1\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_69e22a64c9c4d\">\n        <button class=\"premium-btn-wyjasnienie\"\n                data-id=\"wyjasnienie_69e22a64c9c4d\"\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\n<p><strong>a)<\/strong> Ci\u0105g: a<sub>n<\/sub> = 3\u00b7(1\/2)<sup>n<\/sup> \u2013 takim wzorem okre\u015blony jest ci\u0105g geometryczny.<\/p>\n\n<p><strong>Krok 1 \u2013 pierwszy wyraz:<\/strong><br>\na\u2081 = 3\u00b7(1\/2)<sup>1<\/sup> = 3\/2<br>\nAby obliczy\u0107 pierwszy wyraz ci\u0105gu, do wzoru wstawiamy n = 1 i wykonujemy dzia\u0142anie.<\/p>\n\n<p><strong>Krok 2 \u2013 trzeci wyraz:<\/strong><br>\na\u2083 = 3\u00b7(1\/2)<sup>3<\/sup> = 3\u00b71\/8 = 3\/8<br>\nAby obliczy\u0107 trzeci wyraz ci\u0105gu, do wzoru wstawiamy n = 3 i wykonujemy dzia\u0142anie.<\/p>\n\n<p><strong>Krok 3 \u2013 jedenasty wyraz:<\/strong><br>\na\u2081\u2081 = 3\u00b7(1\/2)<sup>11<\/sup> = 3\u00b71\/2048 = 3\/1024<br>\nAby obliczy\u0107 jedenasty wyraz ci\u0105gu, do wzoru wstawiamy n = 11 i wykonujemy dzia\u0142anie.<\/p>\n\n<hr>\n\n<p><strong>b)<\/strong> Ci\u0105g: a<sub>n<\/sub> = -1\/2\u00b73<sup>n<\/sup> \u2013 takim wzorem okre\u015blony jest ci\u0105g geometryczny.<\/p>\n\n<p><strong>Krok 1 \u2013 pierwszy wyraz:<\/strong><br>\na\u2081 = -1\/2 \u00b7 3<sup>1<\/sup> = -3\/2<br>\nAby obliczy\u0107 pierwszy wyraz ci\u0105gu, do wzoru wstawiamy n = 1 i wykonujemy dzia\u0142anie.<\/p>\n\n<p><strong>Krok 2 \u2013 trzeci wyraz:<\/strong><br>\na\u2083 = -1\/2 \u00b7 3<sup>3<\/sup> = -1\/2 \u00b7 27 = -27\/2<br>\nAby obliczy\u0107 trzeci wyraz ci\u0105gu, do wzoru wstawiamy n = 3 i wykonujemy dzia\u0142anie.<\/p>\n\n<p><strong>Krok 3 \u2013 jedenasty wyraz:<\/strong><br>\na\u2081\u2081 = -1\/2 \u00b7 3<sup>11<\/sup> = -1\/2 \u00b7 177147 = -177147\/2<br>\nAby obliczy\u0107 jedenasty wyraz ci\u0105gu, do wzoru wstawiamy n = 11 i wykonujemy dzia\u0142anie.<\/p>\n\n<hr>\n\n<p><strong>c)<\/strong> Ci\u0105g: a<sub>n<\/sub> = -1024\u00b7(-1\/4)<sup>n-1<\/sup> \u2013 takim wzorem okre\u015blony jest ci\u0105g geometryczny.<\/p>\n\n<p><strong>Krok 1 \u2013 pierwszy wyraz:<\/strong><br>\na\u2081 = -1024\u00b7(-1\/4)<sup>0<\/sup> = -1024<br>\nAby obliczy\u0107 pierwszy wyraz ci\u0105gu, do wzoru wstawiamy n = 1 i wykonujemy dzia\u0142anie.<\/p>\n\n<p><strong>Krok 2 \u2013 trzeci wyraz:<\/strong><br>\na\u2083 = -1024\u00b7(-1\/4)<sup>2<\/sup> = -1024\u00b71\/16 = -64<br>\nAby obliczy\u0107 trzeci wyraz ci\u0105gu, do wzoru wstawiamy n = 3 i wykonujemy dzia\u0142anie.<\/p>\n\n<p><strong>Krok 3 \u2013 jedenasty wyraz:<\/strong><br>\na\u2081\u2081 = -1024\u00b7(-1\/4)<sup>10<\/sup> = -1024\u00b71\/1048576 = -1<br>\nAby obliczy\u0107 jedenasty wyraz ci\u0105gu, do wzoru wstawiamy n = 11 i wykonujemy dzia\u0142anie.<\/p>\n\n        <\/div>\n    <\/div>\n    \n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Oblicz wyrazy a1, a3, a11 ci\u0105gu geometrycznego okre\u015blonego wzorem og\u00f3lnym: a) an = 3\u00b7(1\/2)n b) an = -1\/2\u00b73n c) an = -1024\u00b7(-1\/4)n-1<\/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":[60],"tags":[29,28,59],"class_list":["post-773","post","type-post","status-publish","format-standard","hentry","category-z-d-ciag-geometryczny-obliczanie-wyrazow-ciagu-geometrycznego","tag-ciag-geometryczny","tag-obliczanie-wyrazow-ciagu-geometrycznego","tag-zadania-dodatkowe"],"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":"Oblicz wyrazy a1, a3, a11 ci\u0105gu geometrycznego okre\u015blonego wzorem og\u00f3lnym: a) an = 3\u00b7(1\/2)n b) an = -1\/2\u00b73n c) an = -1024\u00b7(-1\/4)n-1","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/mymatma.pl\/index.php?rest_route=\/wp\/v2\/posts\/773","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=773"}],"version-history":[{"count":13,"href":"https:\/\/mymatma.pl\/index.php?rest_route=\/wp\/v2\/posts\/773\/revisions"}],"predecessor-version":[{"id":816,"href":"https:\/\/mymatma.pl\/index.php?rest_route=\/wp\/v2\/posts\/773\/revisions\/816"}],"wp:attachment":[{"href":"https:\/\/mymatma.pl\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=773"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mymatma.pl\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=773"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mymatma.pl\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=773"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}