**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 \[{\left( -\frac{1}{2} \right)}/{\left( \frac{1}{3} \right)=-\frac{3}{2}}\;\].

*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.

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