# JEE Main & Advanced Mathematics Geometric Progression Definition

## Definition

Category : JEE Main & Advanced

A progression is called a G.P. if the ratio of its each term to its previous term is always constant. This constant ratio is called its common ratio and it is generally denoted by $r$.

Example: The sequence 4, 12, 36, 108, ?.. is a G.P., because $\frac{12}{4}=\frac{36}{12}=\frac{108}{36}=.....=3$, which is constant.

Clearly, this sequence is a G.P. with first term 4 and common ratio 3.

The sequence $\frac{1}{3},\,-\frac{1}{2},\,\frac{3}{4},\,-\frac{9}{8},\,....$ is a G.P. with first term $\frac{1}{3}$ and common ratio ${\left( -\frac{1}{2} \right)}/{\left( \frac{1}{3} \right)=-\frac{3}{2}}\;$.

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