{"id":3630,"date":"2021-10-18T00:12:06","date_gmt":"2021-10-17T22:12:06","guid":{"rendered":"https:\/\/blogsaverroes.juntadeandalucia.es\/recursosdematematicas\/?p=3630"},"modified":"2021-10-18T00:12:06","modified_gmt":"2021-10-17T22:12:06","slug":"sucesion-de-pell","status":"publish","type":"post","link":"https:\/\/blogsaverroes.juntadeandalucia.es\/recursosdematematicas\/sucesion-de-pell\/","title":{"rendered":"Sucesi\u00f3n de Pell"},"content":{"rendered":"<p><span style=\"font-family: 'times new roman', times, serif;font-size: 14pt\">La <strong>sucesi\u00f3n de Pell<\/strong>&nbsp;es una sucesi\u00f3n recurrente de n\u00fameros naturales dada por:<\/span><\/p>\n<p style=\"text-align: center\"><strong><span style=\"font-family: 'times new roman', times, serif;font-size: 14pt\">a<sub>1 <\/sub>= 1&nbsp; &nbsp;,&nbsp; a<sub>2 <\/sub>= 2&nbsp; &nbsp;,&nbsp; a<sub>n <\/sub>= a<sub>n\u20132 <\/sub>+ 2\u00b7a<sub>n\u20131<\/sub><\/span><\/strong><\/p>\n<p style=\"text-align: justify\"><span style=\"font-family: 'times new roman', times, serif;font-size: 14pt\">El primer t\u00e9rmino es igual a 1, el segundo t\u00e9rmino es igual a 2 y, a partir del tercero, cada t\u00e9rmino se obtiene sumando al antepen\u00faltimo el doble del \u00faltimo. <\/span><\/p>\n<table style=\"border-collapse: collapse;width: 100%\">\n<tbody>\n<tr>\n<td style=\"width: 25%;text-align: center\"><span style=\"font-family: 'times new roman', times, serif;font-size: 14pt\">a<sub>3<\/sub>=a<sub>1<\/sub>+2a<sub>2<\/sub>=1+4=<strong>5<\/strong><\/span><\/td>\n<td style=\"width: 25%;text-align: center\"><span style=\"font-family: 'times new roman', times, serif;font-size: 14pt\">a<sub>4<\/sub>=a<sub>2<\/sub>+2a<sub>3<\/sub>=2+10=<strong>12<\/strong><\/span><\/td>\n<td style=\"width: 25%;text-align: center\"><span style=\"font-family: 'times new roman', times, serif;font-size: 14pt\">a<sub>5<\/sub>=a<sub>3<\/sub>+2a<sub>4<\/sub>=5+24=<strong>29<\/strong><\/span><\/td>\n<td style=\"width: 25%;text-align: center\"><span style=\"font-family: 'times new roman', times, serif;font-size: 14pt\">a<sub>6<\/sub>=a<sub>4<\/sub>+2a<sub>5<\/sub>=12+58=<strong>70<\/strong><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 25%;text-align: center\"><span style=\"font-family: 'times new roman', times, serif;font-size: 14pt\">a<sub>7<\/sub>=a<sub>5<\/sub>+2a<sub>6<\/sub>=<strong>169<\/strong><\/span><\/td>\n<td style=\"width: 25%;text-align: center\"><span style=\"font-family: 'times new roman', times, serif;font-size: 14pt\">a<sub>8<\/sub>=a<sub>6<\/sub>+2a<sub>7<\/sub>=<strong>408<\/strong><\/span><\/td>\n<td style=\"width: 25%;text-align: center\"><span style=\"font-family: 'times new roman', times, serif;font-size: 14pt\">a<sub>9<\/sub>=a<sub>7<\/sub>+2a<sub>8<\/sub>=<strong>985<\/strong><\/span><\/td>\n<td style=\"width: 25%;text-align: center\"><span style=\"font-family: 'times new roman', times, serif;font-size: 14pt\">a<sub>10<\/sub>=a<sub>8<\/sub>+2a<sub>9<\/sub>=<strong>2378<\/strong><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: justify\"><span style=\"font-family: 'times new roman', times, serif;font-size: 14pt\">Los quince primeros t\u00e9rminos de la sucesi\u00f3n son:<\/span><\/p>\n<p style=\"text-align: center\"><strong><span style=\"font-family: 'times new roman', times, serif;font-size: 14pt\">1, 2, 5, 12, 29, 70, 169, 408, 985, 2378, 5741, 13860, 33461, 80782, 195025,&nbsp; &#8230;<\/span><\/strong><\/p>\n<p style=\"text-align: justify\"><span style=\"font-family: 'times new roman', times, serif;font-size: 14pt\">Esta sucesi\u00f3n se debe al matem\u00e1tico brit\u00e1nico <strong>John Pell<\/strong> (1611-1685).<\/span><\/p>\n<p style=\"text-align: justify\"><span style=\"font-family: 'times new roman', times, serif;font-size: 14pt\">Se puede obtener la sucesi\u00f3n de Pell de forma gr\u00e1fica con las longitudes de los lados de la siguiente sucesi\u00f3n de cuadrados.<\/span><\/p>\n<p style=\"text-align: center\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-3635\" src=\"https:\/\/blogsaverroes.juntadeandalucia.es\/recursosdematematicas\/files\/2021\/10\/n\u00famero-de-pell.png\" alt=\"\" width=\"729\" height=\"350\" srcset=\"https:\/\/blogsaverroes.juntadeandalucia.es\/recursosdematematicas\/files\/2021\/10\/n\u00famero-de-pell.png 1148w, https:\/\/blogsaverroes.juntadeandalucia.es\/recursosdematematicas\/files\/2021\/10\/n\u00famero-de-pell-300x144.png 300w, https:\/\/blogsaverroes.juntadeandalucia.es\/recursosdematematicas\/files\/2021\/10\/n\u00famero-de-pell-1024x491.png 1024w, https:\/\/blogsaverroes.juntadeandalucia.es\/recursosdematematicas\/files\/2021\/10\/n\u00famero-de-pell-768x369.png 768w\" sizes=\"(max-width: 729px) 100vw, 729px\" \/><\/p>\n","protected":false},"excerpt":{"rendered":"<p>La sucesi\u00f3n de Pell&nbsp;es una sucesi\u00f3n recurrente de n\u00fameros naturales dada por: a1 = 1&nbsp; &nbsp;,&nbsp; a2 = 2&nbsp; &nbsp;,&nbsp; an = an\u20132 + 2\u00b7an\u20131 El primer t\u00e9rmino es igual a 1, el segundo&#46;&#46;&#46;<\/p>\n","protected":false},"author":7927,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"ngg_post_thumbnail":0,"footnotes":""},"categories":[2075204],"tags":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/blogsaverroes.juntadeandalucia.es\/recursosdematematicas\/wp-json\/wp\/v2\/posts\/3630"}],"collection":[{"href":"https:\/\/blogsaverroes.juntadeandalucia.es\/recursosdematematicas\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/blogsaverroes.juntadeandalucia.es\/recursosdematematicas\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/blogsaverroes.juntadeandalucia.es\/recursosdematematicas\/wp-json\/wp\/v2\/users\/7927"}],"replies":[{"embeddable":true,"href":"https:\/\/blogsaverroes.juntadeandalucia.es\/recursosdematematicas\/wp-json\/wp\/v2\/comments?post=3630"}],"version-history":[{"count":5,"href":"https:\/\/blogsaverroes.juntadeandalucia.es\/recursosdematematicas\/wp-json\/wp\/v2\/posts\/3630\/revisions"}],"predecessor-version":[{"id":3636,"href":"https:\/\/blogsaverroes.juntadeandalucia.es\/recursosdematematicas\/wp-json\/wp\/v2\/posts\/3630\/revisions\/3636"}],"wp:attachment":[{"href":"https:\/\/blogsaverroes.juntadeandalucia.es\/recursosdematematicas\/wp-json\/wp\/v2\/media?parent=3630"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blogsaverroes.juntadeandalucia.es\/recursosdematematicas\/wp-json\/wp\/v2\/categories?post=3630"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blogsaverroes.juntadeandalucia.es\/recursosdematematicas\/wp-json\/wp\/v2\/tags?post=3630"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}