The sum [tex]S_{n}[/tex] of n terms of a geometric series with first term [tex]a_{1}[/tex] and common ratio [tex]r[/tex] is given by
[tex]S_{n}=a_{1}\cdot \dfrac{r^{n}-1}{r-1}[/tex]
It can be used in any situation involving the accumulated consequences of exponential growth. In finance, it is used to find the future value of a sequence of payments subject to compound interest.
For example, consider 10 deposits of 1000 made at the end of the year into an account paying 2% compounded annually. The result of such a sequence of payments will be
[tex]S_{10}=\$1000\cdot \dfrac{1.02^{10}-1}{1.02-1}=\$10,949.72[/tex]
