SOLUTION: The sum of an infinite geometric series is 108, while the sum of the first 3 terms is 112. Determine the first term of this series.

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Question 1186218: The sum of an infinite geometric series is 108, while the sum of the first 3 terms is 112. Determine the first term of this series.
Answer by greenestamps(13203) About Me  (Show Source):
You can put this solution on YOUR website!


Let the first term be a and the common ratio be r.

(1) The infinite sum is a%2F%281-r%29

a%2F%281-r%29=108
a=108%281-r%29

The sum of the first three terms is a%2Bar%2Bar%5E2

a%2Bar%2Bar%5E2=112
a%281%2Br%2Br%5E2%29=112
%28108%281-r%29%29%281%2Br%2Br%5E2%29=112
108%281-r%5E3%29=112
1-r%5E3=112%2F108=28%2F27
r%5E3=-1%2F27
r=-1%2F3

a=108%281-r%29+=+108%281%2B1%2F3%29=144

ANSWER: The first term is a = 144.

CHECK:

infinite sum: a%2F%281-r%29=144%2F%281%2B1%2F3%29+=+144%2F%284%2F3%29+=+108

sum of first three terms: 144%2B%28-48%29%2B16+=+112