SOLUTION: S is the sum of the first 2n terms of a GP, if the sum of the alternate terms of the same gp is S/4, find the common ratio of the GP
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Question 858020: S is the sum of the first 2n terms of a GP, if the sum of the alternate terms of the same gp is S/4, find the common ratio of the GP Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website! S is the sum of the first 2n terms of a GP, if the sum of the alternate terms of the same gp is S/4, find the common ratio of the GP
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S(2n) = a[(r^(2n)-1)/(r-1)] = S
S(n) = a[(r^n-1)/(r-1)] = S/4
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Divide S(2n)/S(n) to get:
(r^(2n)-1)/(r^n-1) = 4
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r^(2n)-1 = 4r^n - 4
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(r^n)^2-1-4r^n+4 = 0
(r^n)^2 - 4r^n + 3 = 0
(r^n-1)(r^n-3) = 0
r^n = 1 or r^n = 3
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Cheers,
Stan H.
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