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 Algebra Pre-Algebra and Basic Algebra Math Forum

 January 21st, 2010, 03:52 PM #1 Newbie   Joined: Jan 2010 Posts: 8 Thanks: 0 Sequence Question Kind of new to this site, and don't know if this is the right side, but anyways I'm having trouble with this arithmetic sequence question that is part of my culminating task. If the sum of 'n' terms of an arithmetic sequence is 1/2(n^2+5n) find an expression for the 'k'th term. I'd appreciate it if anyone can show me the steps to solve this question. January 21st, 2010, 04:47 PM #2 Senior Member   Joined: Feb 2009 From: Adelaide, Australia Posts: 1,519 Thanks: 3 Re: Sequence Question To find the first term, let n=1 and apply the formula. To find the second term, let n=2, apply the formula, and subtract the first term. You now have enough information to deduce the sequence. In general, the sum of n terms, with the first term equal to a, will be (a+0b)+(a+1b)+(a+2b)+(a+3b)+...+(a+(n-1)b) = an + �n(n-1)b so you can also equate coefficients. January 21st, 2010, 04:56 PM #3 Newbie   Joined: Jan 2010 Posts: 8 Thanks: 0 Re: Sequence Question ok so the sequence is 3,4,5,6... But what is it meant by the kth term? January 21st, 2010, 05:28 PM #4 Global Moderator   Joined: Oct 2008 From: London, Ontario, Canada - The Forest City Posts: 7,923 Thanks: 1123 Math Focus: Elementary mathematics and beyond Re: Sequence Question The kth term is any term one wishes to choose. Since the sequence is 3, 4, 5, 6, . . . an expression for the kth term would be k + 2. January 22nd, 2010, 12:37 AM #5 Global Moderator   Joined: Dec 2006 Posts: 20,373 Thanks: 2009 The sum of k terms is (k� + 5k)/2. The sum of (k - 1) terms is ((k - 1)� + 5(k - 1))/2. By subtraction, the kth term is (2k - 1 + 5)/2, i.e., k + 2. Tags question, sequence Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post Cryptnar Real Analysis 4 September 29th, 2012 12:07 PM Becarev Real Analysis 1 February 11th, 2012 08:17 AM hermanni Real Analysis 0 February 13th, 2011 12:52 PM rose3 Real Analysis 2 December 31st, 2009 05:35 AM adidasballa95 Algebra 3 May 8th, 2009 08:48 AM

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