{"id":1321,"date":"2025-12-22T14:32:32","date_gmt":"2025-12-22T13:32:32","guid":{"rendered":"http:\/\/mymatma.pl\/?p=1321"},"modified":"2025-12-22T14:32:35","modified_gmt":"2025-12-22T13:32:35","slug":"zadanie-130","status":"publish","type":"post","link":"https:\/\/mymatma.pl\/?p=1321","title":{"rendered":"Zadanie 130"},"content":{"rendered":"\n<p><strong>zadanie 18 \u2013 sierpie\u0144 2020 (1pkt)<\/strong><\/p>\n\n\n\n<p>W ci\u0105gu arytmetycznym (a<sub>n<\/sub>) okre\u015blonym dla ka\u017cdej liczby naturalnej n\u22651 , s\u0105 dane dwa wyrazy: a<sub>1<\/sub>=2 i a<sub>2<\/sub>=5 . St\u0105d wynika, \u017ce n-ty wyraz tego ci\u0105gu jest okre\u015blony wzorem:<\/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>n<\/sub>=3n\u22121<\/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>n<\/sub>=3n+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) a<sub>n<\/sub>=2n+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>n<\/sub>=2n\u22121<\/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_69e23e83dc784\">\n        <button class=\"premium-btn-odp\"\n                data-id=\"odp_69e23e83dc784\"\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) a\u2099 = 3n \u2212 1.\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_69e23e83dc791\">\n        <button class=\"premium-btn-wyjasnienie\"\n                data-id=\"wyjasnienie_69e23e83dc791\"\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 pierwsze wyrazy ci\u0105gu arytmetycznego:<\/p>\n\n<p style=\"text-align:center;\">\na\u2081 = 2, &nbsp; a\u2082 = 5\n<\/p>\n\n<p>W ci\u0105gu arytmetycznym r\u00f3\u017cnica r jest sta\u0142a, wi\u0119c:<\/p>\n\n<p style=\"text-align:center;\">\nr = a\u2082 \u2212 a\u2081 = 5 \u2212 2 = 3\n<\/p>\n\n<h4>Wz\u00f3r na n\u2011ty wyraz ci\u0105gu arytmetycznego<\/h4>\n\n<p style=\"text-align:center;\">\na\u2099 = a\u2081 + (n \u2212 1)r\n<\/p>\n\n<p>Podstawiamy dane warto\u015bci:<\/p>\n\n<p style=\"text-align:center;\">\na\u2099 = 2 + (n \u2212 1)\u00b73\n<\/p>\n\n<p>Upraszczenie:<\/p>\n\n<p style=\"text-align:center;\">\na\u2099 = 2 + 3n \u2212 3 = 3n \u2212 1\n<\/p>\n\n<h3>Odpowied\u017a:<\/h3>\n<p>Wz\u00f3r n\u2011tego wyrazu to <strong>a\u2099 = 3n \u2212 1<\/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 18 \u2013 sierpie\u0144 2020 (1pkt) W ci\u0105gu arytmetycznym (an) okre\u015blonym dla ka\u017cdej liczby naturalnej n\u22651 , s\u0105 dane dwa wyrazy: a1=2 i a2=5 . St\u0105d wynika, \u017ce n-ty wyraz tego ci\u0105gu jest okre\u015blony wzorem: a) an=3n\u22121 b) an=3n+2 c) an=2n+3 d) an=2n\u22121<\/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":[200,203,81,83],"tags":[23,201,202],"class_list":["post-1321","post","type-post","status-publish","format-standard","hentry","category-sierpien-2020","category-wyznaczanie-wzoru-ogolnego","category-zadania-maturalne","category-zadania-tematami","tag-ciag-arytmetyczny","tag-sierpien-2020","tag-wyznaczanie-wzoru-ogolnego"],"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 18 \u2013 sierpie\u0144 2020 (1pkt) W ci\u0105gu arytmetycznym (an) okre\u015blonym dla ka\u017cdej liczby naturalnej n\u22651 , s\u0105 dane dwa wyrazy: a1=2 i a2=5 . St\u0105d wynika, \u017ce n-ty wyraz tego ci\u0105gu jest okre\u015blony wzorem: a) an=3n\u22121 b) an=3n+2 c) an=2n+3 d) an=2n\u22121","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/mymatma.pl\/index.php?rest_route=\/wp\/v2\/posts\/1321","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=1321"}],"version-history":[{"count":1,"href":"https:\/\/mymatma.pl\/index.php?rest_route=\/wp\/v2\/posts\/1321\/revisions"}],"predecessor-version":[{"id":1322,"href":"https:\/\/mymatma.pl\/index.php?rest_route=\/wp\/v2\/posts\/1321\/revisions\/1322"}],"wp:attachment":[{"href":"https:\/\/mymatma.pl\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1321"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mymatma.pl\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1321"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mymatma.pl\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1321"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}