SOLUTION: the sum of the 1st and 2nd term of a geometric progression is 10 while its sum to infinity is 18. find the fourth term

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Question 326512: the sum of the 1st and 2nd term of a geometric progression is 10 while its sum to infinity is 18. find the fourth term
Answer by galactus(183) About Me  (Show Source):
You can put this solution on YOUR website!
The infinite sum is given by a1%2F%281-r%29=18
The nth partial sum is given by a1%28%281-r%5En%29%2F%281-r%29%29
Since we are told the first 2 terms sum to 10, then we have
a1%28%281-r%5E2%29%2F%281-r%29%29=10
But, from the first equation, a1=18%281-r%29
Sub into the second equation:
18%281-r%29%28%281-r%5E2%29%2F%281-r%29%29=10
r=2%2F3
and the first term, a1, is
18%281-2%2F3%29=6
Since the nth term is gven by a1%2Ar%5E%28n-1%29,
The fourth term is
6%2A%282%2F3%29%5E3=16%2F9