{"id":1160,"date":"2025-12-18T12:52:21","date_gmt":"2025-12-18T11:52:21","guid":{"rendered":"http:\/\/mymatma.pl\/?p=1160"},"modified":"2025-12-18T12:52:24","modified_gmt":"2025-12-18T11:52:24","slug":"zadanie-85","status":"publish","type":"post","link":"https:\/\/mymatma.pl\/?p=1160","title":{"rendered":"Zadanie 85"},"content":{"rendered":"\n<p><strong>zadanie 13 \u2013 sierpie\u0144 2018 (1pkt)<\/strong><\/p>\n\n\n\n<p>Ci\u0105g arytmetyczny (a<sub>n<\/sub>) , okre\u015blony dla n\u22651 , spe\u0142nia warunek a<sub>3<\/sub>+a<sub>4<\/sub>+a<sub>5<\/sub>=15 . Wtedy:<\/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) a<sub>4<\/sub> = 5<\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<p>b) a<sub>4<\/sub> = 6<\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<p>c) a<sub>4<\/sub> = 3<\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<p>d) a<sub>4<\/sub> = 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_69e22be98fb8b\">\n        <button class=\"premium-btn-odp\"\n                data-id=\"odp_69e22be98fb8b\"\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<b>a) a\u2084 = 5<\/b>\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_69e22be98fb97\">\n        <button class=\"premium-btn-wyjasnienie\"\n                data-id=\"wyjasnienie_69e22be98fb97\"\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>\nW zadaniu podano, \u017ce ci\u0105g arytmetyczny spe\u0142nia warunek:<br>\na\u2083 + a\u2084 + a\u2085 = 15.\n<br><br>\nKorzystamy ze wzoru na n\u2011ty wyraz ci\u0105gu arytmetycznego:<br>\na\u2099 = a\u2081 + (n \u2212 1)r.\n<br><br>\nZapisujemy kolejne wyrazy wzgl\u0119dem a\u2084:<br>\na\u2083 = a\u2084 \u2212 r<br>\na\u2085 = a\u2084 + r\n<br><br>\nPodstawiamy do r\u00f3wnania:<br>\n(a\u2084 \u2212 r) + a\u2084 + (a\u2084 + r) = 15\n<br><br>\nUpraszcza si\u0119 to do:<br>\n3a\u2084 = 15\n<br><br>\nDzielimy obie strony przez 3:<br>\na\u2084 = 5\n<br><br>\n<strong>Prawid\u0142owa odpowied\u017a: a) 5<\/strong>\n<\/p>\n\n        <\/div>\n    <\/div>\n    \n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>zadanie 13 \u2013 sierpie\u0144 2018 (1pkt) Ci\u0105g arytmetyczny (an) , okre\u015blony dla n\u22651 , spe\u0142nia warunek a3+a4+a5=15 . Wtedy: a) a4 = 5 b) a4 = 6 c) a4 = 3 d) a4 = 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":[25,26,120,81,83],"tags":[23,24,119],"class_list":["post-1160","post","type-post","status-publish","format-standard","hentry","category-ciag-arytmetyczny","category-obliczanie-wyrazow-ciagu","category-sierpien-2018","category-zadania-maturalne","category-zadania-tematami","tag-ciag-arytmetyczny","tag-obliczanie-wyrazow-ciagu","tag-sierpien-2018"],"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 13 \u2013 sierpie\u0144 2018 (1pkt) Ci\u0105g arytmetyczny (an) , okre\u015blony dla n\u22651 , spe\u0142nia warunek a3+a4+a5=15 . Wtedy: a) a4 = 5 b) a4 = 6 c) a4 = 3 d) a4 = 4","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/mymatma.pl\/index.php?rest_route=\/wp\/v2\/posts\/1160","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=1160"}],"version-history":[{"count":1,"href":"https:\/\/mymatma.pl\/index.php?rest_route=\/wp\/v2\/posts\/1160\/revisions"}],"predecessor-version":[{"id":1161,"href":"https:\/\/mymatma.pl\/index.php?rest_route=\/wp\/v2\/posts\/1160\/revisions\/1161"}],"wp:attachment":[{"href":"https:\/\/mymatma.pl\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1160"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mymatma.pl\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1160"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mymatma.pl\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1160"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}