Answer
$13.888,888.75$
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 $a=1.25,\quad r=10$
So, $a_{n}=ar^{n-1} =1.25(10)^{n-1}$
Given the last term, we find n:
$12,500,000=1.25(10)^{n-1}\qquad/\div(1.25)$
$10,000,000=(10)^{n-1}$
$10^{7}=(10)^{n-1}$
$n-1=7$
$n=8$
So
$S_{8}=1.25\displaystyle \cdot\frac{1-(10)^{8}}{1-10}=1.25\cdot\frac{-99999999}{-9}$
$=1.25\cdot 11,111,111$
$=13.888,888.75$
