{"id":6575,"date":"2011-03-02T01:13:27","date_gmt":"2011-03-02T01:13:27","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=6575"},"modified":"2022-01-19T21:15:51","modified_gmt":"2022-01-19T21:15:51","slug":"observa-o-seguinte-triangulo-formado-por-numeros","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=6575","title":{"rendered":"Observa o seguinte tri\u00e2ngulo formado por n\u00fameros"},"content":{"rendered":"<p><ul id='GTTabs_ul_6575' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_6575' class='GTTabs_curr'><a  id=\"6575_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_6575' ><a  id=\"6575_1\" onMouseOver=\"GTTabsShowLinks('Resolu\u00e7\u00e3o'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Resolu\u00e7\u00e3o<\/a><\/li>\n<\/ul>\n\n<div class='GTTabs_divs GTTabs_curr_div' id='GTTabs_0_6575'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>Observa o seguinte tri\u00e2ngulo formado por n\u00fameros.<\/p>\n<p>\\[\\begin{matrix} \u00a0\u00a0 \\text{Linha 1} &amp; {} &amp; {} &amp; {} &amp; {} &amp; 1 &amp; {} &amp; {} &amp; {} &amp; {} &amp; {}\u00a0 \\\\ \u00a0\u00a0 \\text{Linha 2} &amp; {} &amp; {} &amp; {} &amp; 1 &amp; 2 &amp; 1 &amp; {} &amp; {} &amp; {} &amp; {}\u00a0 \\\\ \u00a0\u00a0 \\text{Linha 3} &amp; {} &amp; {} &amp; 1 &amp; 2 &amp; 3 &amp; 2 &amp; 1 &amp; {} &amp; {} &amp; {}\u00a0 \\\\ \u00a0\u00a0 \\text{Linha 4} &amp; {} &amp; 1 &amp; 2 &amp; 3 &amp; 4 &amp; 3 &amp; 2 &amp; 1 &amp; {} &amp; {}\u00a0 \\\\ \u00a0\u00a0 \\text{Linha 5} &amp; 1 &amp; 2 &amp; 3 &amp; 4 &amp; 5 &amp; 4 &amp; 3 &amp; 2 &amp; 1 &amp; {}\u00a0 \\\\ \\end{matrix}\\]<\/p>\n<p>Na 3.\u00aa linha deste tri\u00e2ngulo num\u00e9rico h\u00e1 5 n\u00fameros e na 4.\u00aa linha h\u00e1 7 n\u00fameros.<\/p>\n<p>Quantos n\u00fameros h\u00e1 na 112.\u00aa linha?<br \/>\nExplica como chegaste \u00e0 tua resposta.<\/p>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_6575' onClick='GTTabs_show(1,6575)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_6575'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<p>\\[\\begin{matrix} \u00a0\u00a0 \\text{Linha 1} &amp; {} &amp; {} &amp; {} &amp; {} &amp; 1 &amp; {} &amp; {} &amp; {} &amp; {} &amp; {}\u00a0 \\\\ \u00a0\u00a0 \\text{Linha 2} &amp; {} &amp; {} &amp; {} &amp; 1 &amp; 2 &amp; 1 &amp; {} &amp; {} &amp; {} &amp; {}\u00a0 \\\\ \u00a0\u00a0 \\text{Linha 3} &amp; {} &amp; {} &amp; 1 &amp; 2 &amp; 3 &amp; 2 &amp; 1 &amp; {} &amp; {} &amp; {}\u00a0 \\\\ \u00a0\u00a0 \\text{Linha 4} &amp; {} &amp; 1 &amp; 2 &amp; 3 &amp; 4 &amp; 3 &amp; 2 &amp; 1 &amp; {} &amp; {}\u00a0 \\\\ \u00a0\u00a0 \\text{Linha 5} &amp; 1 &amp; 2 &amp; 3 &amp; 4 &amp; 5 &amp; 4 &amp; 3 &amp; 2 &amp; 1 &amp; {}\u00a0 \\\\ \\end{matrix}\\]<\/p>\n<p>Tabelando a quantidade de n\u00fameros que h\u00e1 em cada uma das primeiras linhas da tabela, obtemos:<\/p>\n<table class=\"aligncenter\" style=\"width: 70%;\" border=\"1\" cellspacing=\"4\" cellpadding=\"2\" align=\"center\">\n<tbody>\n<tr>\n<td>Linha<\/td>\n<td style=\"text-align: center;\">1<\/td>\n<td style=\"text-align: center;\">2<\/td>\n<td style=\"text-align: center;\">3<\/td>\n<td style=\"text-align: center;\">4<\/td>\n<td style=\"text-align: center;\">5<\/td>\n<td style=\"text-align: center;\">6<\/td>\n<td style=\"text-align: center;\">&#8230;<\/td>\n<\/tr>\n<tr>\n<td>Quantidade de n\u00fameros<\/td>\n<td style=\"text-align: center;\">1<\/td>\n<td style=\"text-align: center;\">3<\/td>\n<td style=\"text-align: center;\">5<\/td>\n<td style=\"text-align: center;\">7<\/td>\n<td style=\"text-align: center;\">9<\/td>\n<td style=\"text-align: center;\">11<\/td>\n<td style=\"text-align: center;\">&#8230;<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>A quantidade de n\u00fameros\u00a0na linha seguinte \u00e9 superior em duas unidades \u00e0 da linha anterior, pelo que estamos em presen\u00e7a da sequ\u00eancia dos n\u00fameros naturais \u00edmpares,\u00a0cujo termo geral \u00e9 ${{L}_{n}}=2n-1$.<\/p>\n<p>Assim, na 112.\u00aa linha h\u00e1 ${{L}_{112}}=2\\times 112-1=224-1=223$ n\u00fameros.<\/p><\/p>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_6575' onClick='GTTabs_show(0,6575)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Observa o seguinte tri\u00e2ngulo formado por n\u00fameros.<\/p>\n<p>\\[\\begin{matrix} \u00a0\u00a0 \\text{Linha 1} &#038; {} &#038; {} &#038; {} &#038; {} &#038; 1 &#038; {} &#038; {} &#038; {} &#038; {} &#038; {}\u00a0 \\\\ \u00a0\u00a0 \\text{Linha 2} &#038; {} &#038; {} &#038; {} &#038; 1 &#038; 2 &#038; 1 &#038; {} &#038; {} &#038; {} &#038; {}\u00a0 \\\\ \u00a0\u00a0 \\text{Linha 3} &#038; {} &#038; {} &#038; 1 &#038; 2 &#038; 3 &#038; 2 &#038; 1 &#038; {} &#038; {} &#038; {}\u00a0 \\\\ \u00a0\u00a0 \\text{Linha 4} &#038; {} &#038; 1 &#038; 2 &#038; 3 &#038; 4 &#038; 3 &#038; 2 &#038; 1 &#038; {} &#038; {}\u00a0 \\\\ \u00a0\u00a0 \\text{Linha 5} &#038; 1 &#038; 2 &#038; 3 &#038; 4 &#038; 5 &#038; 4 &#038; 3 &#038; 2 &#038; 1 &#038; {}\u00a0 \\\\ \\end{matrix}\\]<\/p>\n<p>Na 3.\u00aa linha deste tri\u00e2ngulo num\u00e9rico h\u00e1 5 n\u00fameros e na 4.\u00aa linha h\u00e1 7 n\u00fameros.<\/p>\n<p>Quantos n\u00fameros h\u00e1 na 112.\u00aa linha?<br \/>\nExplica como chegaste \u00e0 tua resposta.<\/p>\n","protected":false},"author":1,"featured_media":19189,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[100,137,97],"tags":[138],"series":[],"class_list":["post-6575","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-8--ano","category-ainda-os-numeros","category-aplicando","tag-sequencias"],"views":1230,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2021\/12\/Mat75.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/6575","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=6575"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/6575\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/19189"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=6575"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=6575"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=6575"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=6575"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}