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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