{"id":1256,"date":"2025-12-22T12:01:14","date_gmt":"2025-12-22T11:01:14","guid":{"rendered":"http:\/\/mymatma.pl\/?p=1256"},"modified":"2025-12-22T12:01:17","modified_gmt":"2025-12-22T11:01:17","slug":"zadanie-109","status":"publish","type":"post","link":"https:\/\/mymatma.pl\/?p=1256","title":{"rendered":"Zadanie 109"},"content":{"rendered":"\n<p><strong>zadanie 11 \u2013 sierpie\u0144 2019 (1pkt)<\/strong><\/p>\n\n\n\n<p><br>W ci\u0105gu arytmetycznym (a<sub>n<\/sub>) , okre\u015blonym dla n\u22651 , dane s\u0105 wyrazy: a<sub>1<\/sub>=\u221211 i a<sub>9<\/sub>=5 . Suma dziewi\u0119ciu 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) -24<\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<p>b) -27<\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<p>c) -16<\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<p>d) -18<\/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_69e22a960892f\">\n        <button class=\"premium-btn-odp\"\n                data-id=\"odp_69e22a960892f\"\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) -24.\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_69e22a960893b\">\n        <button class=\"premium-btn-wyjasnienie\"\n                data-id=\"wyjasnienie_69e22a960893b\"\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> = -11<\/li>\n  <li>a<sub>9<\/sub> = 5<\/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 = 9:<\/p>\n\n<p style=\"text-align:center;\">\n5 = -11 + 8r\n<\/p>\n\n<p>Dodajemy 11 do obu stron:<\/p>\n\n<p style=\"text-align:center;\">\n16 = 8r\n<\/p>\n\n<p>Dzielimy przez 8:<\/p>\n\n<p style=\"text-align:center;\">\nr = 2\n<\/p>\n\n<p>Teraz obliczamy sum\u0119 dziewi\u0119ciu pierwszych wyraz\u00f3w:<\/p>\n\n<p style=\"text-align:center;\">\nS<sub>9<\/sub> = (a<sub>1<\/sub> + a<sub>9<\/sub>) \u00b7 9 \/ 2\n<\/p>\n\n<p>Podstawiamy warto\u015bci:<\/p>\n\n<p style=\"text-align:center;\">\nS<sub>9<\/sub> = (-11 + 5) \u00b7 9 \/ 2\n<\/p>\n\n<p style=\"text-align:center;\">\nS<sub>9<\/sub> = (-6) \u00b7 9 \/ 2 = -54 \/ 2 = -27\n<\/p>\n\n<h3>Odpowied\u017a:<\/h3>\n<p>Suma dziewi\u0119ciu pierwszych wyraz\u00f3w wynosi <strong>-27<\/strong>.<\/p>\n\n        <\/div>\n    <\/div>\n    \n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>zadanie 11 \u2013 sierpie\u0144 2019 (1pkt) W ci\u0105gu arytmetycznym (an) , okre\u015blonym dla n\u22651 , dane s\u0105 wyrazy: a1=\u221211 i a9=5 . Suma dziewi\u0119ciu pocz\u0105tkowych wyraz\u00f3w tego ci\u0105gu jest r\u00f3wna: a) -24 b) -27 c) -16 d) -18<\/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":[25,62,195,81,83],"tags":[23,61,131],"class_list":["post-1256","post","type-post","status-publish","format-standard","hentry","category-ciag-arytmetyczny","category-sierpien-2019","category-suma-poczatkowych-wyrazow-ciagu-ciag-arytmetyczny","category-zadania-maturalne","category-zadania-tematami","tag-ciag-arytmetyczny","tag-sierpien-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 sierpie\u0144 2019 (1pkt) W ci\u0105gu arytmetycznym (an) , okre\u015blonym dla n\u22651 , dane s\u0105 wyrazy: a1=\u221211 i a9=5 . Suma dziewi\u0119ciu pocz\u0105tkowych wyraz\u00f3w tego ci\u0105gu jest r\u00f3wna: a) -24 b) -27 c) -16 d) -18","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/mymatma.pl\/index.php?rest_route=\/wp\/v2\/posts\/1256","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=1256"}],"version-history":[{"count":1,"href":"https:\/\/mymatma.pl\/index.php?rest_route=\/wp\/v2\/posts\/1256\/revisions"}],"predecessor-version":[{"id":1258,"href":"https:\/\/mymatma.pl\/index.php?rest_route=\/wp\/v2\/posts\/1256\/revisions\/1258"}],"wp:attachment":[{"href":"https:\/\/mymatma.pl\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1256"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mymatma.pl\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1256"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mymatma.pl\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1256"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}