# Geometric Sequence

## Geometric Sequence

Sequence in which the ratio r, not equal to 1, of two consecutive terms is a constant.

Synonym for geometric progression.

The constant ratio r is called the ratio of the geometric sequence.

### Example

If an amount M is invested at an interest rate of i% compounded annually, then the sequence of values of this investment after n years is given by : S = {M · (0.01i), M · (0.01i)², M · (0.01i)³, …}. The common ratio r of this sequence is r = 1 + 0.01 · i or r = 1.01 · i.

The value of this investment after n years is given by $$M · (1 + 0.01 · i)^n$$ or $$M · (1.01 · i)^n$$.