SOLUTION: Find the sum of the series 4 + 12 + 36 + ….. + 8748.

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Question 1186917: Find the sum of the series 4 + 12 + 36 + ….. + 8748.
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

We know the first term is 4, so
a%5B1%5D=4
Each term is 3 times bigger than the last, meaning we have a%5B1%5Dr%5E%28n-1%29, with r=3
So, we know the series follows 4%283%29%5E%28n-1%29.
Foe a geometric series:
S%5Bn%5D=a%5B1%5D%28%281-r%5En%29%2F%281-r%29%29
we have: a%5B1%5D=4 and r=3
We need n for the last term:
4%283%29%5E%28n-1%29=8748
3%5E%28n-1%29=2187.......since 2187=3%5E7
3%5E%28n-1%29=3%5E7........since bases same, equal the exponents
n-1=7
n=8
S%5B8%5D=4%28%281-3%5E8%29%2F%281-3%29%29
S%5B8%5D=4%28%28-6560%29%2F%28-2%29%29
S%5B8%5D=4%283280%29
S%5B8%5D=13120