Answer
$S_{8}=13,888,888.75$
Work Step by Step
We are asked to find the sum of:
$1.25+12.5+125+\cdots+12,500,000$
We see that this is a geometric sequence with $a_1=1.25$. We find $r$:
$r=12.5/1.25=10$
We know that a geometric sequence has the form:
$a_{n}=ar^{n-1}$
We use this to find $n$:
$a_n=(1.25)(10)^{n-1}$
$12500000=(1.25)(10)^{n-1}$
$10000000=(10)^{n-1}$
$n-1=7$
$n=8$
We know the partial sum of a geometric sequence is:
$S_n=a_1\frac{1-r^n}{1-r}$
$S_{8}=1.25 \frac{1-10^{8}}{1-10}=13,888,888.75$
