SOLUTION: an arithmetic progression has the 8th term being twice the 4th term. if the 20th term is 40, find the sum of the first 20 terms of the series.

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Question 1003374: an arithmetic progression has the 8th term being twice the 4th term. if the 20th term is 40, find the sum of the first 20 terms of the series.
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
nth. term of an AP is a+(n-1) d
a8 = a+7d
a4 = a+3d
2(a+3d) = a+7d
2a+6d = a+7d
a=d
a20 = a+19d
40 = a+19a
20a=40
a= 2
d=2
Sn = %28n%2F2%29%282a%2B%28n-1%29d%29
S20 = %2820%2F2%29%2A%282%2A2%2B19%2A2%29
= 10(4+38)
10*42
=420
S20 = 420