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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+(n1)b) = an + ½n(n1)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: 7,767 Thanks: 1017 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: 18,719 Thanks: 1536 
The sum of k terms is (k² + 5k)/2. The sum of (k  1) terms is ((k  1)² + 5(k  1))/2. By subtraction, the kth term is (2k  1 + 5)/2, i.e., k + 2. 

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