SOLUTION: The sum to infinity of a GP is twice the sum of the first two terms. Find possible values of the common ratio.

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Question 1163035: The sum to infinity of a GP is twice the sum of the first two terms.
Find possible values of the common ratio.
Answer by greenestamps(13203) About Me  (Show Source):
You can put this solution on YOUR website!


With first term a and common ratio r....

the sum of the first two terms is a%2Bar;
the infinite sum is a%2F%281-r%29

The condition is that the infinite sum be twice the sum of the first two terms:

a%2F%281-r%29+=+2%28a%2Bar%29
1%2F%281-r%29+=+2%281%2Br%29
1%2F2+=+1-r%5E2
r%5E2+=+1%2F2
r+=+sqrt%282%29%2F2 or r+=+-sqrt%282%29%2F2

Both solutions satisfy the condition of the problem.

ANSWER: The possible common ratios are sqrt%282%29%2F2 and -sqrt%282%29%2F2