{"id":1259,"date":"2025-12-22T12:06:59","date_gmt":"2025-12-22T11:06:59","guid":{"rendered":"http:\/\/mymatma.pl\/?p=1259"},"modified":"2025-12-22T12:07:03","modified_gmt":"2025-12-22T11:07:03","slug":"zadanie-110","status":"publish","type":"post","link":"https:\/\/mymatma.pl\/?p=1259","title":{"rendered":"Zadanie 110"},"content":{"rendered":"\n<p><strong>zadanie 11 \u2013 maj 2019 (1pkt)<\/strong><\/p>\n\n\n\n<p>W ci\u0105gu arytmetycznym a<sub>n<\/sub> , okre\u015blonym dla n\u22651 , dane s\u0105 dwa wyrazy: a<sub>1<\/sub>=7 i a<sub>8<\/sub>=\u221249 . Suma o\u015bmiu pocz\u0105tkowych wyraz\u00f3w tego ci\u0105gu jest r\u00f3wna:<\/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) -168<\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<p>b) -189<\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<p>c) -21<\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<p>d) -42<\/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_69e22be9262fc\">\n        <button class=\"premium-btn-odp\"\n                data-id=\"odp_69e22be9262fc\"\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 b) -189.\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_69e22be926307\">\n        <button class=\"premium-btn-wyjasnienie\"\n                data-id=\"wyjasnienie_69e22be926307\"\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 podano dwa wyrazy ci\u0105gu arytmetycznego:<\/p>\n\n<ul>\n  <li>a<sub>1<\/sub> = 7<\/li>\n  <li>a<sub>8<\/sub> = -49<\/li>\n<\/ul>\n\n<p>Korzystamy ze wzoru na n\u2011ty wyraz ci\u0105gu arytmetycznego:<\/p>\n\n<p style=\"text-align:center;\">\na<sub>n<\/sub> = a<sub>1<\/sub> + (n \u2212 1)r\n<\/p>\n\n<p>Podstawiamy dane dla n = 8:<\/p>\n\n<p style=\"text-align:center;\">\n-49 = 7 + 7r\n<\/p>\n\n<p>Odejmujemy 7 od obu stron:<\/p>\n\n<p style=\"text-align:center;\">\n-56 = 7r\n<\/p>\n\n<p>Dzielimy przez 7:<\/p>\n\n<p style=\"text-align:center;\">\nr = -8\n<\/p>\n\n<p>Teraz obliczamy sum\u0119 o\u015bmiu pierwszych wyraz\u00f3w:<\/p>\n\n<p style=\"text-align:center;\">\nS<sub>8<\/sub> = (a<sub>1<\/sub> + a<sub>8<\/sub>) \u00b7 8 \/ 2\n<\/p>\n\n<p>Podstawiamy warto\u015bci:<\/p>\n\n<p style=\"text-align:center;\">\nS<sub>8<\/sub> = (7 + (-49)) \u00b7 8 \/ 2\n<\/p>\n\n<p style=\"text-align:center;\">\nS<sub>8<\/sub> = (-42) \u00b7 4 = -168\n<\/p>\n\n<h3>Odpowied\u017a:<\/h3>\n<p>Suma o\u015bmiu pierwszych wyraz\u00f3w wynosi <strong>-168<\/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 11 \u2013 maj 2019 (1pkt) W ci\u0105gu arytmetycznym an , okre\u015blonym dla n\u22651 , dane s\u0105 dwa wyrazy: a1=7 i a8=\u221249 . Suma o\u015bmiu pocz\u0105tkowych wyraz\u00f3w tego ci\u0105gu jest r\u00f3wna: a) -168 b) -189 c) -21 d) -42<\/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":[25,64,195,81,83],"tags":[23,63,131],"class_list":["post-1259","post","type-post","status-publish","format-standard","hentry","category-ciag-arytmetyczny","category-maj-2019","category-suma-poczatkowych-wyrazow-ciagu-ciag-arytmetyczny","category-zadania-maturalne","category-zadania-tematami","tag-ciag-arytmetyczny","tag-maj-2019","tag-suma-poczatkowych-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 11 \u2013 maj 2019 (1pkt) W ci\u0105gu arytmetycznym an , okre\u015blonym dla n\u22651 , dane s\u0105 dwa wyrazy: a1=7 i a8=\u221249 . Suma o\u015bmiu pocz\u0105tkowych wyraz\u00f3w tego ci\u0105gu jest r\u00f3wna: a) -168 b) -189 c) -21 d) -42","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/mymatma.pl\/index.php?rest_route=\/wp\/v2\/posts\/1259","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=1259"}],"version-history":[{"count":1,"href":"https:\/\/mymatma.pl\/index.php?rest_route=\/wp\/v2\/posts\/1259\/revisions"}],"predecessor-version":[{"id":1262,"href":"https:\/\/mymatma.pl\/index.php?rest_route=\/wp\/v2\/posts\/1259\/revisions\/1262"}],"wp:attachment":[{"href":"https:\/\/mymatma.pl\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1259"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mymatma.pl\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1259"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mymatma.pl\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1259"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}