Question

What is the formula for a finite geometric series and how can use it in a practical situation

Answer 1

The sum
`S_(n)` of n terms of a geometric series with first term
`a_(1)` and common ratio
`r` is given by

`S_(n)=a_(1)\cdot (r^(n)-1)/(r-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 (1.02^(10)-1)/(1.02-1)=\$10,949.72`