# JEE Main & Advanced Mathematics Geometric Progression General term of a G.P.

## General term of a G.P.

Category : JEE Main & Advanced

(1) We know that, $a,\,ar,\,a{{r}^{2}},\,a{{r}^{3}},\,.....a{{r}^{n-1}}$ is a sequence of G.P.

Here, the first term is ‘a’ and the common ratio is $'r'$.

The general term or ${{n}^{th}}$ term of a G.P. is ${{T}_{n}}=a{{r}^{n-1}}$.

It should be noted that, $r=\frac{{{T}_{2}}}{{{T}_{1}}}=\frac{{{T}_{3}}}{{{T}_{2}}}=......$.

(2) ${{p}^{th}}$ term from the end of a finite G.P. : If G.P. consists of $'n'$ terms, ${{p}^{th}}$ term from the end $={{(n-p+1)}^{th}}$ term from the beginning $=a{{r}^{n-p}}$.

Also, the ${{p}^{th}}$ term from the end of a G.P. with last term $l$and common ratio $r$ is $l\,{{\left( \frac{1}{r} \right)}^{n-1}}$.

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