{"id":309,"date":"2020-04-27T03:05:00","date_gmt":"2020-04-27T03:05:00","guid":{"rendered":"https:\/\/sites.ps.uci.edu\/mathceo\/?page_id=309"},"modified":"2020-05-16T22:20:00","modified_gmt":"2020-05-16T22:20:00","slug":"number-sequences","status":"publish","type":"page","link":"https:\/\/sites.ps.uci.edu\/mathceo-old\/meeting-2\/number-sequences\/","title":{"rendered":"Number Sequences"},"content":{"rendered":"\n<p>A list of numbers ordered on a line is called a number <em><strong>sequence<\/strong><\/em>. Probably the first number sequence that you learned is<\/p>\n\n\n\n<div class=\"wp-block-group has-subtle-background-background-color has-background\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<p style=\"font-size:28px\" class=\"has-text-align-center\">1, 2, 3, 4, 5, 6, 7, 8, 9, 10, &#8230;.     <\/p>\n\n\n\n<p class=\"has-text-color has-text-align-center has-accent-color\">&#8220;One, two, three, four, five, six, seven, eight, nine, ten, &#8230;..&#8221;<\/p>\n<\/div><\/div>\n\n\n\n<p> <\/p>\n\n\n\n<hr class=\"wp-block-separator\" \/>\n\n\n\n<p>The numbers of a sequence can come from anywhere. For instance, you can read them off from a chart:<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"585\" height=\"384\" src=\"https:\/\/sites.ps.uci.edu\/mathceo\/wp-content\/uploads\/sites\/18\/2020\/04\/bar_graph.png\" alt=\"\" class=\"wp-image-240\" srcset=\"https:\/\/sites.ps.uci.edu\/mathceo-old\/wp-content\/uploads\/sites\/18\/2020\/04\/bar_graph.png 585w, https:\/\/sites.ps.uci.edu\/mathceo-old\/wp-content\/uploads\/sites\/18\/2020\/04\/bar_graph-300x197.png 300w, https:\/\/sites.ps.uci.edu\/mathceo-old\/wp-content\/uploads\/sites\/18\/2020\/04\/bar_graph-500x328.png 500w\" sizes=\"auto, (max-width: 585px) 100vw, 585px\" \/><\/figure><\/div>\n\n\n\n<p>Reading across from left to right, we have here a sequence of just five numbers: 5, 3, 7, 8, 6.<\/p>\n\n\n\n<hr class=\"wp-block-separator\" \/>\n\n\n\n<p>Let&#8217;s make our own number sequences. We can write down the sequences on a <a rel=\"noreferrer noopener\" href=\"https:\/\/docs.google.com\/spreadsheets\/d\/1ONSGeS_1WtEGXXj27iw9Y_X-uYhO1f_7jROHjekEPrA\/edit?usp=sharing\" target=\"_blank\">Google sheet<\/a>.<\/p>\n\n\n\n<ul class=\"wp-block-list\"><li><strong>Birthday sequence:<\/strong> a list the month of the year of each group member, and separately, the day of the month<\/li><li><strong>Favorite number:<\/strong> everyone say their favorite number(s)<\/li><li><strong>Digits of the number Pi :<\/strong> \u03a0 = 3 . 1 4 1 5 1 9 2 6 5 3 5 9 . . .<\/li><\/ul>\n\n\n\n<hr class=\"wp-block-separator\" \/>\n\n\n\n<h4 class=\"has-text-align-center wp-block-heading\">Number Sequences with a Pattern<\/h4>\n\n\n\n<p>Sometimes, the number sequences comes with a pattern. Let&#8217;s try to find a pattern and predict the next three numbers for each of the sequences below.<\/p>\n\n\n\n<p class=\"has-large-font-size\">(A) 2, 4, 6, 8, 10, \u2026.<\/p>\n\n\n\n<p class=\"has-large-font-size\">(B) 3, -6, 9, -12, 15, -18, \u2026<\/p>\n\n\n\n<p class=\"has-large-font-size\">(C) 5, 13, 21, 29, 37 , \u2026<\/p>\n\n\n\n<p class=\"has-large-font-size\">(D) 1, 2, 4, 8, 16, 32, \u2026<\/p>\n\n\n\n<p class=\"has-large-font-size\">(E) 2, 3, 5, 8, 12, 17, \u2026<\/p>\n\n\n\n<p><\/p>\n\n\n\n<p>Example (D) is an <strong>exponential<\/strong> type sequence. Every successive number increases (or decreases) by multiplying a fixed number. In this example, each number of the sequence can be written as some number &#8220;X&#8221; raised to a power (or <strong>exponent<\/strong>). What number is &#8220;X&#8221;?<\/p>\n","protected":false},"excerpt":{"rendered":"<p>A list of numbers ordered on a line is called a number sequence. Probably the first number sequence that you learned is 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, &#8230;. &#8220;One, two, three, four, five, six, seven, eight, nine, ten, &#8230;..&#8221; The numbers of a sequence can come from anywhere. For instance, [&hellip;]<\/p>\n","protected":false},"author":16,"featured_media":0,"parent":218,"menu_order":1,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_vp_format_video_url":"","_vp_image_focal_point":[],"footnotes":""},"class_list":["post-309","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/sites.ps.uci.edu\/mathceo-old\/wp-json\/wp\/v2\/pages\/309","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/sites.ps.uci.edu\/mathceo-old\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/sites.ps.uci.edu\/mathceo-old\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/sites.ps.uci.edu\/mathceo-old\/wp-json\/wp\/v2\/users\/16"}],"replies":[{"embeddable":true,"href":"https:\/\/sites.ps.uci.edu\/mathceo-old\/wp-json\/wp\/v2\/comments?post=309"}],"version-history":[{"count":3,"href":"https:\/\/sites.ps.uci.edu\/mathceo-old\/wp-json\/wp\/v2\/pages\/309\/revisions"}],"predecessor-version":[{"id":313,"href":"https:\/\/sites.ps.uci.edu\/mathceo-old\/wp-json\/wp\/v2\/pages\/309\/revisions\/313"}],"up":[{"embeddable":true,"href":"https:\/\/sites.ps.uci.edu\/mathceo-old\/wp-json\/wp\/v2\/pages\/218"}],"wp:attachment":[{"href":"https:\/\/sites.ps.uci.edu\/mathceo-old\/wp-json\/wp\/v2\/media?parent=309"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}