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 · (0.01*i*), M · (0.01*i*)², M · (0.01*i*)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 \(M · (1.01 · i)^n\).