Answer
$11,999.99988$
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}$
---------------
We see that $a=10,800,\displaystyle \quad r=\frac{1}{10}=10^{-1}$
So, $a_{n}=ar^{n-1} =10,800(\displaystyle \frac{1}{10})^{n-1}$
Given the last term, we find n:
$0.000108=10800(\displaystyle \frac{1}{10})^{n-1}\qquad/\div(10800)$
$10^{-8}=(10^{-1})^{n-1}$
$(10^{-1})^{8}=(10^{-1})^{n-1}$
$n-1=8$
$n=9$
So
$S_{8}=10,800\displaystyle \cdot\frac{1-(10^{-1})^{9}}{1-\frac{1}{10}}=11,999.99988$
