{"id":1590,"date":"2025-12-31T12:56:06","date_gmt":"2025-12-31T11:56:06","guid":{"rendered":"http:\/\/mymatma.pl\/?p=1590"},"modified":"2025-12-31T12:56:09","modified_gmt":"2025-12-31T11:56:09","slug":"zadanie-154","status":"publish","type":"post","link":"https:\/\/mymatma.pl\/?p=1590","title":{"rendered":"Zadanie 154"},"content":{"rendered":"\n<p><strong>zadanie 16 &#8211; grudzie\u0144 2014 (1pkt)<\/strong><\/p>\n\n\n\n<p>Na \u015bcianie kamienicy zaprojektowano mural utworzony z szeregu tr\u00f3jk\u0105t\u00f3w r\u00f3wnobocznych r\u00f3\u017cnej wielko\u015bci. Najmniejszy tr\u00f3jk\u0105t ma bok d\u0142ugo\u015bci&nbsp;1m, a bok ka\u017cdego z nast\u0119pnych tr\u00f3jk\u0105t\u00f3w jest o&nbsp;10cm&nbsp;d\u0142u\u017cszy ni\u017c bok poprzedzaj\u0105cego go tr\u00f3jk\u0105ta. Ostatni tr\u00f3jk\u0105t ma bok d\u0142ugo\u015bci&nbsp;5,9m. Ile tr\u00f3jk\u0105t\u00f3w przedstawia mural?<\/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) 49<\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<p>b) 50<\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<p>c) 59<\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<p>d) 60<\/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_69e22b9d5e380\">\n        <button class=\"premium-btn-odp\"\n                data-id=\"odp_69e22b9d5e380\"\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) 50.\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_69e22b9d5e38b\">\n        <button class=\"premium-btn-wyjasnienie\"\n                data-id=\"wyjasnienie_69e22b9d5e38b\"\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<h2>Wyja\u015bnienie<\/h2>\n\n<p>W zadaniu mamy ci\u0105g d\u0142ugo\u015bci bok\u00f3w tr\u00f3jk\u0105t\u00f3w r\u00f3wnobocznych. Pierwszy tr\u00f3jk\u0105t ma bok:<\/p>\n\n<p><strong>1 m<\/strong><\/p>\n\n<p>Ka\u017cdy kolejny tr\u00f3jk\u0105t ma bok d\u0142u\u017cszy o:<\/p>\n\n<p><strong>10 cm = 0,1 m<\/strong><\/p>\n\n<p>Ostatni tr\u00f3jk\u0105t ma bok:<\/p>\n\n<p><strong>5,9 m<\/strong><\/p>\n\n<h3>Krok 1: Zapisujemy wz\u00f3r na n-ty wyraz ci\u0105gu arytmetycznego<\/h3>\n\n<p>\na\u2099 = a\u2081 + (n \u2212 1)\u00b7r  \n<\/p>\n\n<p>Podstawiamy dane:<\/p>\n\n<p>\n5,9 = 1 + (n \u2212 1)\u00b70,1\n<\/p>\n\n<h3>Krok 2: Rozwi\u0105zujemy r\u00f3wnanie<\/h3>\n\n<p>\n5,9 \u2212 1 = (n \u2212 1)\u00b70,1  \n<\/p>\n\n<p>\n4,9 = 0,1(n \u2212 1)\n<\/p>\n\n<p>\n49 = n \u2212 1\n<\/p>\n\n<p>\nn = 50\n<\/p>\n\n<h3>Wniosek<\/h3>\n\n<p>Mural przedstawia <strong>50 tr\u00f3jk\u0105t\u00f3w<\/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 16 &#8211; grudzie\u0144 2014 (1pkt) Na \u015bcianie kamienicy zaprojektowano mural utworzony z szeregu tr\u00f3jk\u0105t\u00f3w r\u00f3wnobocznych r\u00f3\u017cnej wielko\u015bci. Najmniejszy tr\u00f3jk\u0105t ma bok d\u0142ugo\u015bci&nbsp;1m, a bok ka\u017cdego z nast\u0119pnych tr\u00f3jk\u0105t\u00f3w jest o&nbsp;10cm&nbsp;d\u0142u\u017cszy ni\u017c bok poprzedzaj\u0105cego go tr\u00f3jk\u0105ta. Ostatni tr\u00f3jk\u0105t ma bok d\u0142ugo\u015bci&nbsp;5,9m. Ile tr\u00f3jk\u0105t\u00f3w przedstawia mural? a) 49 b) 50 c) 59 d) 60<\/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":[25,266,204,81,83],"tags":[23,268,205],"class_list":["post-1590","post","type-post","status-publish","format-standard","hentry","category-ciag-arytmetyczny","category-grudzien-2014","category-rozne","category-zadania-maturalne","category-zadania-tematami","tag-ciag-arytmetyczny","tag-grudzien-2014","tag-rozne"],"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 16 &#8211; grudzie\u0144 2014 (1pkt) Na \u015bcianie kamienicy zaprojektowano mural utworzony z szeregu tr\u00f3jk\u0105t\u00f3w r\u00f3wnobocznych r\u00f3\u017cnej wielko\u015bci. Najmniejszy tr\u00f3jk\u0105t ma bok d\u0142ugo\u015bci&nbsp;1m, a bok ka\u017cdego z nast\u0119pnych tr\u00f3jk\u0105t\u00f3w jest o&nbsp;10cm&nbsp;d\u0142u\u017cszy ni\u017c bok poprzedzaj\u0105cego go tr\u00f3jk\u0105ta. Ostatni tr\u00f3jk\u0105t ma bok d\u0142ugo\u015bci&nbsp;5,9m. Ile tr\u00f3jk\u0105t\u00f3w przedstawia mural? a) 49 b) 50 c) 59 d) 60","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/mymatma.pl\/index.php?rest_route=\/wp\/v2\/posts\/1590","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=1590"}],"version-history":[{"count":1,"href":"https:\/\/mymatma.pl\/index.php?rest_route=\/wp\/v2\/posts\/1590\/revisions"}],"predecessor-version":[{"id":1594,"href":"https:\/\/mymatma.pl\/index.php?rest_route=\/wp\/v2\/posts\/1590\/revisions\/1594"}],"wp:attachment":[{"href":"https:\/\/mymatma.pl\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1590"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mymatma.pl\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1590"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mymatma.pl\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1590"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}