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.


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 \(M · (1.01 · i)^n\).

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