SOLUTION: given that the sum of the first two terms of a geometric progression is 90 and the sum to infinity is 640/7,find the two possible values of the common ratio

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Question 1112775: given that the sum of the first two terms of a geometric progression is 90 and the sum to infinity is 640/7,find the two possible values of the common ratio
Answer by ikleyn(52792) About Me  (Show Source):
You can put this solution on YOUR website!
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We are given  a+%2B+ar = 90,   or  a%2A%281%2Br%29 = 90,   or  a = 90%2F%281%2Br%29.


We are also given that  a%2F%281-r%29 = 640%2F7,   or   a = %28640%2F7%29%2A%281-r%29.


Since left sides of the two last equations are identical, their right sides are equal:

90%2F%281%2Br%29 = %28640%2F7%29%2A%281-r%29,


which implies

90*7 = 640%2A%281-r%5E2%29,

63 = 64+-+64%2Ar%5E2   ====>  64r%5E2 = 64 - 63 = 1  ====>  r%5E2 = 1%2F64  ====>  r = +/- sqrt%281%2F64%29 = +/- 1%2F8.


Answer.  The two value of the common ratio are  +/-1%2F8.

Solved.