**Geometric mean:**

If a, b, c are in G.P . Then middle term of this G.P is known as geometric mean of a G.P.

let b be geometric mean in a, b, c .

b^{2} = a.c

1. Single geometric mean of n positive numbers :

Let G be the geometric mean of n positive numbers—

a1 , a2 , a3 , ……… , an.

G = (a1.a2.a3…..an )^{1/n}

For n = 2

In a , G , b are in G.P

G = √ab

2. n Geometric mean between two numbers :

Let G1 , G2 , G3 , ……. , Gn be the Geometric mean between a and b.

Then ,

a , G1 , G2 , G3 , ………. , Gn , b will be in G.P.

here ,

a = 1st term

let r = common ratio

b = ( n + 2) th term of an G.P

b = a.r^{n+2-1}

r = ( b / a )^{1/n+1}

G1 = ar = a. ( b / a )^{1/n+1}

G2 = a.r^{2 = }a.(b / a )^{2/n+1}

^{:}

Gn = a.r^{n = }a.( b / a )^{n/n+1}

Gn = a.( b / a )^{n/n+1}