How can you use the formula for a finite geometric series in a practical situation?

The finite geometric series formula is a(1-rⁿ)/(1-r).

The sum S_{n}Sn of n terms of a geometric series with first term a_{1}a1 and common ratio rr is given by

S_{n}=a_{1}\cdot \dfrac{r^{n}-1}{r-1}Sn=a1⋅r−1rn−1

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

S_{10}=\$1000\cdot \dfrac{1.02^{10}-1}{1.02-1}=\$10,949.72S10=$1000⋅1.02−11.0210−1=$10,949.72

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