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(52794)   (Show Source): You can put this solution on YOUR website!
.
We are given   = 90,   or   = 90,   or  a = .


We are also given that   = ,   or   a = .


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

 = ,


which implies

90*7 = ,

63 =    ====>   = 64 - 63 = 1  ====>   =   ====>  r = +/-  = +/- .


Answer.  The two value of the common ratio are  +/-.

Solved.


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