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

Algebra ->  Sequences-and-series -> 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      Log On


   

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) About Me  (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)
-------
and the sum of the series.
S(n) = (7+7k)[(5+3k)+(17+17k)]/2
-----
S(n) = 7(1+k)(17(1+k))/2
-----
S(n) = (119/2)*(1+k)^2
------
S(n) = 59.5(1+k)^2
------
Cheers,
Stan H.
----------