If a, b, c are in A.P. then show that 3a, 3b, 3c are in G.P.

Solution :

If a, b, c are in A.P, then b = (a + c)/2

In G.P, b = √ac

To prove that 3a, 3b, 3c are in G.P.

3b = √(3a ⋅ 3c)

3b = (3a + c)1/2

3b = 3(a+c)/2

b = (a + c)/2

Hence 3a, 3b, 3c are in G.P.