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January 21st, 2010, 03:52 PM   #1
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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.
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January 21st, 2010, 04:47 PM   #2
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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
= an + Żn(n-1)b
so you can also equate coefficients.
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January 21st, 2010, 04:56 PM   #3
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Re: Sequence Question

ok so the sequence is 3,4,5,6...

But what is it meant by the kth term?
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January 21st, 2010, 05:28 PM   #4
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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.
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January 22nd, 2010, 12:37 AM   #5
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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.
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