{"id":1424,"date":"2025-12-31T08:14:34","date_gmt":"2025-12-31T07:14:34","guid":{"rendered":"http:\/\/mymatma.pl\/?p=1424"},"modified":"2025-12-31T08:14:37","modified_gmt":"2025-12-31T07:14:37","slug":"zadanie-144","status":"publish","type":"post","link":"https:\/\/mymatma.pl\/?p=1424","title":{"rendered":"Zadanie 144"},"content":{"rendered":"\n<p><strong>zadanie 30 \u2013 listopad 2009 ( zadanie otwarte) (2pkt)<\/strong><\/p>\n\n\n\n<p>Wyka\u017c, \u017ce dla ka\u017cdego m ci\u0105g (m+1)\/4 , (m+3)\/6 , (m+9)\/12 jest arytmetyczny.<\/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_69e22bbb9b381\">\n        <button class=\"premium-btn-odp\"\n                data-id=\"odp_69e22bbb9b381\"\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            \n<p>Ci\u0105g jest arytmetyczny, bo oba r\u00f3\u017cnice s\u0105 r\u00f3wne: <strong>d = -1\/12<\/strong>.<\/p>\n\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_69e22bbb9b38d\">\n        <button class=\"premium-btn-wyjasnienie\"\n                data-id=\"wyjasnienie_69e22bbb9b38d\"\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<p>Rozwa\u017camy trzy kolejne wyrazy ci\u0105gu:<\/p>\n\n<p>\na\u2081 = (m + 1) \/ 4<br>\na\u2082 = (m + 3) \/ 6<br>\na\u2083 = (m + 9) \/ 12\n<\/p>\n\n<h3>Krok 1: Obliczenie r\u00f3\u017cnicy a\u2082 \u2212 a\u2081<\/h3>\n\n<p>\na\u2082 \u2212 a\u2081 = (m+3)\/6 \u2212 (m+1)\/4\n<\/p>\n\n<p>Sprowadzamy do wsp\u00f3lnego mianownika 12:<\/p>\n\n<p>\n= (2(m+3) \u2212 3(m+1)) \/ 12<br>\n= (2m + 6 \u2212 3m \u2212 3) \/ 12<br>\n= (\u2212m + 3) \/ 12\n<\/p>\n\n<h3>Krok 2: Obliczenie r\u00f3\u017cnicy a\u2083 \u2212 a\u2082<\/h3>\n\n<p>\na\u2083 \u2212 a\u2082 = (m+9)\/12 \u2212 (m+3)\/6\n<\/p>\n\n<p>Sprowadzamy do wsp\u00f3lnego mianownika 12:<\/p>\n\n<p>\n= (m+9 \u2212 2(m+3)) \/ 12<br>\n= (m + 9 \u2212 2m \u2212 6) \/ 12<br>\n= (\u2212m + 3) \/ 12\n<\/p>\n\n<h3>Krok 3: Por\u00f3wnanie r\u00f3\u017cnic<\/h3>\n\n<p>\na\u2082 \u2212 a\u2081 = (\u2212m + 3) \/ 12<br>\na\u2083 \u2212 a\u2082 = (\u2212m + 3) \/ 12\n<\/p>\n\n<p>R\u00f3\u017cnice s\u0105 r\u00f3wne dla ka\u017cdego m.<\/p>\n\n<h3>Wniosek<\/h3>\n\n<p><strong>Ci\u0105g jest arytmetyczny, poniewa\u017c r\u00f3\u017cnica mi\u0119dzy kolejnymi wyrazami jest sta\u0142a.<\/strong><\/p>\n\n        <\/div>\n    <\/div>\n    \n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>zadanie 30 \u2013 listopad 2009 ( zadanie otwarte) (2pkt) Wyka\u017c, \u017ce dla ka\u017cdego m ci\u0105g (m+1)\/4 , (m+3)\/6 , (m+9)\/12 jest arytmetyczny.<\/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":[25,88,204,81,83],"tags":[23,87,205],"class_list":["post-1424","post","type-post","status-publish","format-standard","hentry","category-ciag-arytmetyczny","category-listopad-2009","category-rozne","category-zadania-maturalne","category-zadania-tematami","tag-ciag-arytmetyczny","tag-listopad-2009","tag-rozne"],"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 30 \u2013 listopad 2009 ( zadanie otwarte) (2pkt) Wyka\u017c, \u017ce dla ka\u017cdego m ci\u0105g (m+1)\/4 , (m+3)\/6 , (m+9)\/12 jest arytmetyczny.","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/mymatma.pl\/index.php?rest_route=\/wp\/v2\/posts\/1424","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=1424"}],"version-history":[{"count":1,"href":"https:\/\/mymatma.pl\/index.php?rest_route=\/wp\/v2\/posts\/1424\/revisions"}],"predecessor-version":[{"id":1430,"href":"https:\/\/mymatma.pl\/index.php?rest_route=\/wp\/v2\/posts\/1424\/revisions\/1430"}],"wp:attachment":[{"href":"https:\/\/mymatma.pl\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1424"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mymatma.pl\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1424"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mymatma.pl\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1424"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}