SOLUTION: The first term of an arithmetic series is (5+3k), where k is a positive integer. The last term is 17(1+k) and the common difference is 2. Find, in terms of k, the number of terms i

Question 1035274: The first term of an arithmetic series is (5+3k), where k is a positive integer. The last term is 17(1+k) and the common difference is 2. Find, in terms of k, the number of terms in the series and the sum of the series.
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
The first term of an arithmetic series is (5+3k), where k is a positive integer. The last term is 17(1+k) and the common difference is 2.
Find, in terms of k,
the number of terms in the series
17(1+k) = (5+3k)+(n-1)2
17 + 17k = 5+3k+2n-2
2n = 17-3 + 17k-3k
2n = 14 + 14k
n = 7+7k (that is the number of terms)
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and the sum of the series.
S(n) = (7+7k)[(5+3k)+(17+17k)]/2
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S(n) = 7(1+k)(17(1+k))/2
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S(n) = (119/2)*(1+k)^2
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S(n) = 59.5(1+k)^2
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Cheers,
Stan H.
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