# Geometric Progression (G.P.)

If '

*a*' is the first term and '*r*' is the common ratio, then a G.P. can be written as,*a*,*ar*,*ar*^{2},*ar*^{3}, ........ .Note that

*a*,*b*,*c*are in G.**P. â‡”***b*^{2}=*ac***General term of a G. P. :**

General term (

*n*^{th}term) of a G.P. is given by T*=*_{n}*ar*^{n}^{â€“1}**Sum of n terms of a G. P. :**

The sum of first

*n*terms of a G.P. is given byS

*= , when*_{n}*r*< 1or S

*= , when*_{n}*r*> 1 and S*=*_{n}*na*, when*r*= 1**Sum of an infinite G. P. :**

The sum of an infinite G.P. with first term

*a*and common ratio*r*such that |*r*| < 1,S

_{âˆž }=**Geometric mean (g. m.)**

If G be the G.M. between two given quantities a and b then a, G,

*b*, are in G.P.i.e. â‡’ G

^{2}=*ab*â‡’ G =