{"id":20584,"date":"2017-03-19T19:50:18","date_gmt":"2017-03-19T19:50:18","guid":{"rendered":"http:\/\/www.oracletutoring.ca\/blog\/?p=20584"},"modified":"2017-03-19T19:50:18","modified_gmt":"2017-03-19T19:50:18","slug":"math-geometric-sequences-increasing-difference-when-r1","status":"publish","type":"post","link":"https:\/\/www.oracletutoring.ca\/blog\/math-geometric-sequences-increasing-difference-when-r1\/","title":{"rendered":"Math:  geometric sequences:  increasing difference when r>1"},"content":{"rendered":"<h1>Tutoring math, geometric sequences are commonly encountered.<\/h1>\n<p>You&#8217;ll find an introduction to geometric sequences in my post <a href=\"?p=12351\">here.<\/a><\/p>\n<p><strong>Example:<\/strong>  Let&#8217;s imagine a geometric sequence with ratio r greater than one and start term M\/r.  It runs<\/p>\n<p>M\/r, M, Mr&#8230;.<\/p>\n<p>Can we be sure that the successive differences always increase?<\/p>\n<p>Solution:<\/p>\n<p>We need to show that Mr-M > M-M\/r.<\/p>\n<p>We get a common denominator for M-M\/r:<\/p>\n<p>M-M\/r=(Mr-M)\/r<\/p>\n<p>Since r>1, (Mr-M) > (Mr-M)\/r.  Since (Mr-M)\/r = M-M\/r, we see that, indeed, Mr-M > M-M\/r.  When r>1, the differences between successive terms in a geometric sequence must continually increase.<\/p>\n<p>Source:<\/p>\n<p>Travers, Kenneth et al.  <u>Using Advanced Algebra<\/u>.  Toronto:  Doubleday, 1977.<\/p>\n<p>Jack of <a href=\"https:\/\/www.oracletutoring.ca\">Oracle Tutoring by Jack and Diane,<\/a> Campbell River, BC.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Tutoring math, geometric sequences are commonly encountered. You&#8217;ll find an introduction to geometric sequences in my post here. Example: Let&#8217;s imagine a geometric sequence with ratio r greater than one and start term M\/r. It runs M\/r, M, Mr&#8230;. Can &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"more-link\" href=\"https:\/\/www.oracletutoring.ca\/blog\/math-geometric-sequences-increasing-difference-when-r1\/\"> <span class=\"screen-reader-text\">Math:  geometric sequences:  increasing difference when r>1<\/span> Read More &raquo;<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[3],"tags":[1053,2178],"class_list":["post-20584","post","type-post","status-publish","format-standard","hentry","category-math","tag-geometric-sequence","tag-r1"],"_links":{"self":[{"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/posts\/20584","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/comments?post=20584"}],"version-history":[{"count":10,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/posts\/20584\/revisions"}],"predecessor-version":[{"id":20594,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/posts\/20584\/revisions\/20594"}],"wp:attachment":[{"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/media?parent=20584"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/categories?post=20584"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/tags?post=20584"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}