{"id":1244,"date":"2025-12-22T11:17:49","date_gmt":"2025-12-22T10:17:49","guid":{"rendered":"http:\/\/mymatma.pl\/?p=1244"},"modified":"2025-12-22T11:17:54","modified_gmt":"2025-12-22T10:17:54","slug":"zadanie-104","status":"publish","type":"post","link":"https:\/\/mymatma.pl\/?p=1244","title":{"rendered":"Zadanie 104"},"content":{"rendered":"\n<p><strong>zadanie 29 \u2013 czerwiec 2014 ( zadanie otwarte) (2pkt)<\/strong><\/p>\n\n\n\n<p>Liczby 6,2x+4,x+26 w podanej kolejno\u015bci s\u0105 pierwszym, drugim i trzecim wyrazem pewnego ci\u0105gu arytmetycznego. Oblicz r\u00f3\u017cnic\u0119 r tego ci\u0105gu.<\/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_69e22b3e1cb9e\">\n        <button class=\"premium-btn-odp\"\n                data-id=\"odp_69e22b3e1cb9e\"\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 r = 20.\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_69e22b3e1cba9\">\n        <button class=\"premium-btn-wyjasnienie\"\n                data-id=\"wyjasnienie_69e22b3e1cba9\"\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<h3>Wyja\u015bnienie<\/h3>\n\n<p>W ci\u0105gu arytmetycznym r\u00f3\u017cnica r jest sta\u0142a, wi\u0119c:<\/p>\n\n<p style=\"text-align:center;\">\na<sub>2<\/sub> \u2212 a<sub>1<\/sub> = a<sub>3<\/sub> \u2212 a<sub>2<\/sub>\n<\/p>\n\n<p>Podstawiamy dane wyrazy:<\/p>\n\n<ul>\n  <li>a<sub>1<\/sub> = 6<\/li>\n  <li>a<sub>2<\/sub> = 2x + 4<\/li>\n  <li>a<sub>3<\/sub> = x + 26<\/li>\n<\/ul>\n\n<p>Uk\u0142adamy r\u00f3wnanie:<\/p>\n\n<p style=\"text-align:center;\">\n(2x + 4) \u2212 6 = (x + 26) \u2212 (2x + 4)\n<\/p>\n\n<p>Upraszczamy obie strony:<\/p>\n\n<p style=\"text-align:center;\">\n2x \u2212 2 = \u2212x + 22\n<\/p>\n\n<p>Dodajemy x do obu stron:<\/p>\n\n<p style=\"text-align:center;\">\n3x \u2212 2 = 22\n<\/p>\n\n<p>Dodajemy 2:<\/p>\n\n<p style=\"text-align:center;\">\n3x = 24\n<\/p>\n\n<p>St\u0105d:<\/p>\n\n<p style=\"text-align:center; font-size: 1.2em;\">\n<strong>x = 8<\/strong>\n<\/p>\n\n<p>Teraz obliczamy r\u00f3\u017cnic\u0119 r:<\/p>\n\n<p style=\"text-align:center;\">\nr = a<sub>2<\/sub> \u2212 a<sub>1<\/sub> = (2\u00b78 + 4) \u2212 6 = 20\n<\/p>\n\n<h3>Odpowied\u017a:<\/h3>\n<p>r = 20<\/p>\n\n        <\/div>\n    <\/div>\n    \n<\/div>\n<\/div>\n\n\n\n<p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>zadanie 29 \u2013 czerwiec 2014 ( zadanie otwarte) (2pkt) Liczby 6,2x+4,x+26 w podanej kolejno\u015bci s\u0105 pierwszym, drugim i trzecim wyrazem pewnego ci\u0105gu arytmetycznego. Oblicz r\u00f3\u017cnic\u0119 r tego ci\u0105gu.<\/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":[25,141,160,81,83],"tags":[23,140,161],"class_list":["post-1244","post","type-post","status-publish","format-standard","hentry","category-ciag-arytmetyczny","category-czerwiec-2014","category-obliczanie-roznicy-ciagu","category-zadania-maturalne","category-zadania-tematami","tag-ciag-arytmetyczny","tag-czerwiec-2014","tag-obliczanie-roznicy-ciagu"],"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 29 \u2013 czerwiec 2014 ( zadanie otwarte) (2pkt) Liczby 6,2x+4,x+26 w podanej kolejno\u015bci s\u0105 pierwszym, drugim i trzecim wyrazem pewnego ci\u0105gu arytmetycznego. Oblicz r\u00f3\u017cnic\u0119 r tego ci\u0105gu.","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/mymatma.pl\/index.php?rest_route=\/wp\/v2\/posts\/1244","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=1244"}],"version-history":[{"count":1,"href":"https:\/\/mymatma.pl\/index.php?rest_route=\/wp\/v2\/posts\/1244\/revisions"}],"predecessor-version":[{"id":1245,"href":"https:\/\/mymatma.pl\/index.php?rest_route=\/wp\/v2\/posts\/1244\/revisions\/1245"}],"wp:attachment":[{"href":"https:\/\/mymatma.pl\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1244"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mymatma.pl\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1244"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mymatma.pl\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1244"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}