{"id":1168,"date":"2025-12-18T13:26:58","date_gmt":"2025-12-18T12:26:58","guid":{"rendered":"http:\/\/mymatma.pl\/?p=1168"},"modified":"2025-12-18T13:27:00","modified_gmt":"2025-12-18T12:27:00","slug":"zadanie-89","status":"publish","type":"post","link":"https:\/\/mymatma.pl\/?p=1168","title":{"rendered":"Zadanie 89"},"content":{"rendered":"\n<p><strong>zadanie 14 \u2013 maj 2016 (1pkt)<\/strong><\/p>\n\n\n\n<p>Czternasty wyraz ci\u0105gu arytmetycznego jest r\u00f3wny 8 , a r\u00f3\u017cnica tego ci\u0105gu jest r\u00f3wna \u2212(3\/2) . Si\u00f3dmy wyraz tego ci\u0105gu jest r\u00f3wny:<\/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) 37\/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) \u2013 (37\/2)<\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<p>c) \u2013 (5\/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) 5\/2<\/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_69e22ba16a45f\">\n        <button class=\"premium-btn-odp\"\n                data-id=\"odp_69e22ba16a45f\"\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) 37\/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_69e22ba16a46a\">\n        <button class=\"premium-btn-wyjasnienie\"\n                data-id=\"wyjasnienie_69e22ba16a46a\"\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:<br>\na\u2081\u2084 = 8 oraz r = -\\(\\frac{3}{2}\\).\n<\/p>\n\n<p>\nKorzystamy ze wzoru na n\u2011ty wyraz ci\u0105gu arytmetycznego:<br>\na\u2099 = a\u2081 + (n \u2212 1)r.\n<\/p>\n\n<p>\nNajpierw obliczamy a\u2081 z r\u00f3wnania dla a\u2081\u2084:<br>\na\u2081 + 13r = 8<br>\na\u2081 + 13 \u00b7 (-3\/2) = 8<br>\na\u2081 &#8211; 39\/2 = 8<br>\na\u2081 = 8 + 39\/2 = 16\/2 + 39\/2 = 55\/2\n<\/p>\n\n<p>\nTeraz obliczamy si\u00f3dmy wyraz:<br>\na\u2087 = a\u2081 + 6r<br>\na\u2087 = 55\/2 + 6 \u00b7 (-3\/2)<br>\na\u2087 = 55\/2 &#8211; 18\/2 = 37\/2\n<\/p>\n\n<p><strong>Prawid\u0142owa odpowied\u017a: 37\/2<\/strong><\/p>\n\n        <\/div>\n    <\/div>\n    \n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>zadanie 14 \u2013 maj 2016 (1pkt) Czternasty wyraz ci\u0105gu arytmetycznego jest r\u00f3wny 8 , a r\u00f3\u017cnica tego ci\u0105gu jest r\u00f3wna \u2212(3\/2) . Si\u00f3dmy wyraz tego ci\u0105gu jest r\u00f3wny: a) 37\/2 b) \u2013 (37\/2) c) \u2013 (5\/2) d) 5\/2<\/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":[25,122,26,81,83],"tags":[23,121,24],"class_list":["post-1168","post","type-post","status-publish","format-standard","hentry","category-ciag-arytmetyczny","category-maj-2016","category-obliczanie-wyrazow-ciagu","category-zadania-maturalne","category-zadania-tematami","tag-ciag-arytmetyczny","tag-maj-2016","tag-obliczanie-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 14 \u2013 maj 2016 (1pkt) Czternasty wyraz ci\u0105gu arytmetycznego jest r\u00f3wny 8 , a r\u00f3\u017cnica tego ci\u0105gu jest r\u00f3wna \u2212(3\/2) . Si\u00f3dmy wyraz tego ci\u0105gu jest r\u00f3wny: a) 37\/2 b) \u2013 (37\/2) c) \u2013 (5\/2) d) 5\/2","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/mymatma.pl\/index.php?rest_route=\/wp\/v2\/posts\/1168","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=1168"}],"version-history":[{"count":1,"href":"https:\/\/mymatma.pl\/index.php?rest_route=\/wp\/v2\/posts\/1168\/revisions"}],"predecessor-version":[{"id":1169,"href":"https:\/\/mymatma.pl\/index.php?rest_route=\/wp\/v2\/posts\/1168\/revisions\/1169"}],"wp:attachment":[{"href":"https:\/\/mymatma.pl\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1168"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mymatma.pl\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1168"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mymatma.pl\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1168"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}