Question 896823: I can't seem to figure out how to start with this problem...
The sum of the first two terms of a geometric sequence is 9. The sum to infinity of the corresponding geometric series is 12. Find all possible values of the first term and the common ratio.
Answer by rothauserc(4718)   (Show Source):
You can put this solution on YOUR website! Geometric sequence is defined as
Xn = ar^(n-1)
in our case a = 6 and r = 1/2 and the geometric sequence looks like
6, 3, 3/2, 3/4, .....
the sum of a geometric sequence to infinity is defined as
a(1-r^n / 1-r)
note as n goes to infinity (1/2)^n approaches 0, then we have
6*(1/ 1/2) = 6*2 = 12
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