{"id":1303,"date":"2025-12-22T13:29:16","date_gmt":"2025-12-22T12:29:16","guid":{"rendered":"http:\/\/mymatma.pl\/?p=1303"},"modified":"2025-12-22T13:29:21","modified_gmt":"2025-12-22T12:29:21","slug":"zadanie-122","status":"publish","type":"post","link":"https:\/\/mymatma.pl\/?p=1303","title":{"rendered":"Zadanie 122"},"content":{"rendered":"\n<p><strong>zadanie 16 \u2013 grudzie\u0144 2022 (1pkt)<\/strong><\/p>\n\n\n\n<p>Pi\u0119ciowyrazowy ci\u0105g (\u22123,1\/2,x,y,11) jest arytmetyczny. Liczby x oraz y s\u0105 r\u00f3wne:<\/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<p>a) x =4 oraz y = 15\/2<\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<p>b) x = 15\/2 oraz y = 4<\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<p>c) x = -4 oraz y = 15\/2<\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<p>d) x = -(15\/2) oraz y = 4<\/p>\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_69e22b3fcb862\">\n        <button class=\"premium-btn-odp\"\n                data-id=\"odp_69e22b3fcb862\"\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 a) x = 4 oraz y = 15\/2.\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_69e22b3fcb870\">\n        <button class=\"premium-btn-wyjasnienie\"\n                data-id=\"wyjasnienie_69e22b3fcb870\"\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 zadaniu dany jest pi\u0119ciowyrazowy ci\u0105g arytmetyczny:<\/p>\n\n<p style=\"text-align:center;\">\n(\u22123, &nbsp; 1\/2, &nbsp; x, &nbsp; y, &nbsp; 11)\n<\/p>\n\n<p>Aby ci\u0105g by\u0142 arytmetyczny, r\u00f3\u017cnica mi\u0119dzy kolejnymi wyrazami musi by\u0107 sta\u0142a. Najpierw obliczamy r\u00f3\u017cnic\u0119 na podstawie dw\u00f3ch pierwszych wyraz\u00f3w:<\/p>\n\n<p style=\"text-align:center;\">\nr = \\(\\frac{1}{2}\\) \u2212 (\u22123) = \\(\\frac{1}{2}\\) + 3 = \\(\\frac{7}{2}\\)\n<\/p>\n\n<h4>1. Obliczamy x<\/h4>\n\n<p>Trzeci wyraz powstaje przez dodanie r\u00f3\u017cnicy do drugiego:<\/p>\n\n<p style=\"text-align:center;\">\nx = \\(\\frac{1}{2}\\) + \\(\\frac{7}{2}\\) = \\(\\frac{8}{2}\\) = 4\n<\/p>\n\n<h4>2. Obliczamy y<\/h4>\n\n<p>Czwarty wyraz to:<\/p>\n\n<p style=\"text-align:center;\">\ny = x + r = 4 + \\(\\frac{7}{2}\\) = \\(\\frac{8}{2} + \\frac{7}{2}\\) = \\(\\frac{15}{2}\\)\n<\/p>\n\n<h3>Odpowied\u017a:<\/h3>\n<p>x = <strong>4<\/strong> oraz y = <strong>15\/2<\/strong>.<\/p>\n\n        <\/div>\n    <\/div>\n    \n<\/div>\n<\/div>\n\n\n\n<p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>zadanie 16 \u2013 grudzie\u0144 2022 (1pkt) Pi\u0119ciowyrazowy ci\u0105g (\u22123,1\/2,x,y,11) jest arytmetyczny. Liczby x oraz y s\u0105 r\u00f3wne: a) x =4 oraz y = 15\/2 b) x = 15\/2 oraz y = 4 c) x = -4 oraz y = 15\/2 d) x = -(15\/2) oraz y = 4<\/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":[25,90,198,81,83],"tags":[23,89,197],"class_list":["post-1303","post","type-post","status-publish","format-standard","hentry","category-ciag-arytmetyczny","category-grudzien-2022","category-wlasnosci-trzech-kolejnych-wyrazow-ciagu","category-zadania-maturalne","category-zadania-tematami","tag-ciag-arytmetyczny","tag-grudzien-2022","tag-wlasnosci-trzech-kolejnych-wyrazow-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 16 \u2013 grudzie\u0144 2022 (1pkt) Pi\u0119ciowyrazowy ci\u0105g (\u22123,1\/2,x,y,11) jest arytmetyczny. Liczby x oraz y s\u0105 r\u00f3wne: a) x =4 oraz y = 15\/2 b) x = 15\/2 oraz y = 4 c) x = -4 oraz y = 15\/2 d) x = -(15\/2) oraz y = 4","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/mymatma.pl\/index.php?rest_route=\/wp\/v2\/posts\/1303","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=1303"}],"version-history":[{"count":1,"href":"https:\/\/mymatma.pl\/index.php?rest_route=\/wp\/v2\/posts\/1303\/revisions"}],"predecessor-version":[{"id":1304,"href":"https:\/\/mymatma.pl\/index.php?rest_route=\/wp\/v2\/posts\/1303\/revisions\/1304"}],"wp:attachment":[{"href":"https:\/\/mymatma.pl\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1303"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mymatma.pl\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1303"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mymatma.pl\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1303"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}