**Given :**

**A1 and A**_{2} are two AM between a and b.

**Let d be the common difference of this A.P. Clearly, it contains (n+2) terms = 2+2 = 4 terms
**

=> b = (n+2)th term = 4th term

**Now, Putting the value of n = 2 in A**_{1} and A_{2} we get,

**A**_{1} = (2a+b) / 3 -------------(1)

**A**_{2} = (a+2b) / 3 -------------(2)

**Fro question :**

**=> (2A1 – A2)*(2A2-A1) = [2(2a+b)/3-(a+2b)/3] * [2/3(a+2b)-(2a+b)/3]**

**=> (2A1 – A2)*(2A2-A1) = ab**