Answer
$3280$
Work Step by Step
See p. 861.
For the geometric sequence $a_{n}=ar^{n-1}$
the nth partial sum$ S_{n}=\displaystyle \sum_{k=1}^{n}ar^{k-1}$ (where $r\neq 1$)
is given by$ \displaystyle \quad S_{n}=a\cdot\frac{1-r^{n}}{1-r}$
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We see that $a=1, r=\displaystyle \frac{3}{1}=\frac{9}{3}=3.$
So, $a_{n}=ar^{n-1} =1\times 3^{n-1}=3^{n-1}$
Given the last term, we find n:
$2187=3^{n-1}$
Factoring, $2187=3\times 729=3^{2}\times 243=...=3^{7}$
$3^{n-1}=3^{7}$
$n=8$
We can use the formula for $S_{8}$,
$S_{8}=(1)\displaystyle \frac{1-3^{8}}{1-3}=3280$.
