**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 \[l\,{{\left( \frac{1}{r} \right)}^{n-1}}\].

*play_arrow*Definition*play_arrow*General term of a G.P.*play_arrow*Selection of Terms in a G.P.*play_arrow*Sum of first 'n' terms of a G.P.*play_arrow*Sum of infinite terms of a G.P.*play_arrow*Geometric Mean*play_arrow*Properties of G.P.*play_arrow*Definition*play_arrow*\[{{n}^{th}}\]term of A.G.P.*play_arrow*Sum of A.G.P.*play_arrow*Method for Finding Sum*play_arrow*Method of Difference*play_arrow*Special Series*play_arrow*Properties of Arithmetic, Geometric, Harmonic Means Between Two Given Numbers*play_arrow*Relation Between A.P., G.P. and H.P.

You need to login to perform this action.

You will be redirected in
3 sec

Free

Videos

Videos