**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}**