SOLUTION: the sum to infinity of a geometric progression is twice the sum of the first two terms. find possible values of the common ratio.

Question 761611: the sum to infinity of a geometric progression is twice the sum of the first two terms. find possible values of the common ratio.
Found 2 solutions by stanbon, ramkikk66:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
the sum to infinity of a geometric progression is twice the sum of the first two terms. find possible values of the common ratio.
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S to infinity = a/(1-r)
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Equation:
a/(1-r) = 2(a + ar)
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a = 2a(1+r)(1-r)
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2(1-r^2) = 1
1-r^2 = -1
r^2 = 2
r = +/-sqrt(2)
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Cheers,
Stan H.
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Answer by ramkikk66(644) (Show Source): You can put this solution on YOUR website!
Similar to problem 463319.
If 'a' is the first term, and 'r' the common ratio of the GP,
the sum to infinity is given by the formula

Cancelling out a from both sides

Simplifying:

or
:)

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