{"id":1121,"date":"2025-12-18T10:32:07","date_gmt":"2025-12-18T09:32:07","guid":{"rendered":"http:\/\/mymatma.pl\/?p=1121"},"modified":"2025-12-18T12:38:40","modified_gmt":"2025-12-18T11:38:40","slug":"zadanie-78","status":"publish","type":"post","link":"https:\/\/mymatma.pl\/?p=1121","title":{"rendered":"Zadanie 78"},"content":{"rendered":"\n<p><strong>zadanie 17 \u2013 czerwiec 2024 (1 pkt)<\/strong><\/p>\n\n\n\n<p>W ci\u0105gu arytmetycznym (a<sub>n<\/sub>) , okre\u015blonym dla ka\u017cdej liczby naturalnej n\u22651 , dane s\u0105 wyrazy: a<sub>1<\/sub>=7 oraz a<sub>2<\/sub>=13. Wyraz a<sub>10<\/sub> 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) -47<\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<p>b) 52<\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<p>c) 61<\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<p>d) 67<\/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_69e227b0c485e\">\n        <button class=\"premium-btn-odp\"\n                data-id=\"odp_69e227b0c485e\"\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>c) 61<\/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_69e227b0c4869\">\n        <button class=\"premium-btn-wyjasnienie\"\n                data-id=\"wyjasnienie_69e227b0c4869\"\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>\nDany jest ci\u0105g arytmetyczny o wyrazach: <strong>a\u2081 = 7<\/strong> oraz <strong>a\u2082 = 13<\/strong>.  \nNajpierw obliczamy r\u00f3\u017cnic\u0119 ci\u0105gu:\n<br><br>\nr = a\u2082 \u2212 a\u2081 = 13 \u2212 7 = 6\n<br><br>\nKorzystamy ze wzoru na n\u2011ty wyraz ci\u0105gu arytmetycznego:\n<br>\na\u2099 = a\u2081 + (n \u2212 1)r\n<br><br>\nPodstawiamy n = 10:\n<br>\na\u2081\u2080 = 7 + 9 \u00b7 6 = 7 + 54 = 61\n<br><br>\n<strong>Prawid\u0142owa odpowied\u017a: c) 61<\/strong>\n<\/p>\n\n        <\/div>\n    <\/div>\n    \n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>zadanie 17 \u2013 czerwiec 2024 (1 pkt) W ci\u0105gu arytmetycznym (an) , okre\u015blonym dla ka\u017cdej liczby naturalnej n\u22651 , dane s\u0105 wyrazy: a1=7 oraz a2=13. Wyraz a10 jest r\u00f3wny: a) -47 b) 52 c) 61 d) 67<\/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":[25,104,26,81,83],"tags":[23,103,24],"class_list":["post-1121","post","type-post","status-publish","format-standard","hentry","category-ciag-arytmetyczny","category-czerwiec-2024","category-obliczanie-wyrazow-ciagu","category-zadania-maturalne","category-zadania-tematami","tag-ciag-arytmetyczny","tag-czerwiec-2024","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 17 \u2013 czerwiec 2024 (1 pkt) W ci\u0105gu arytmetycznym (an) , okre\u015blonym dla ka\u017cdej liczby naturalnej n\u22651 , dane s\u0105 wyrazy: a1=7 oraz a2=13. Wyraz a10 jest r\u00f3wny: a) -47 b) 52 c) 61 d) 67","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/mymatma.pl\/index.php?rest_route=\/wp\/v2\/posts\/1121","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=1121"}],"version-history":[{"count":2,"href":"https:\/\/mymatma.pl\/index.php?rest_route=\/wp\/v2\/posts\/1121\/revisions"}],"predecessor-version":[{"id":1148,"href":"https:\/\/mymatma.pl\/index.php?rest_route=\/wp\/v2\/posts\/1121\/revisions\/1148"}],"wp:attachment":[{"href":"https:\/\/mymatma.pl\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1121"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mymatma.pl\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1121"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mymatma.pl\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1121"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}