Q10 of 176 Page 20

If a, b, c are in G.P., prove that the following are also in G.P. :
a², b², c²

As a, b, c are in G.P.

Therefore

b² = ac … (1)

We have to prove a², b², c² are in GP or

we need to prove: (b²)² = (ac)² {using idea of GM}

On squaring equation 1 we get,

⇒ b⁴ = a²c²

⇒ (b²)² = (ac)²

Hence a²,b²,c² are in GP.

If a, b, c, d are in G.P, prove that :

(a + b + c + d)² = (a + b)² + 2(b + c)² + (c + d)²

If a, b, c, d are in G.P, prove that :

(b + c) (b + d) = (c + a) (c + d)

If a, b, c are in G.P., prove that the following are also in G.P. :

a³, b³, c³

If a, b, c are in G.P., prove that the following are also in G.P. :

a² + b², ab + bc, b² + c²

If a, b, c are in G.P., prove that the following are also in G.P. :a2, b2, c2