Q10 of 176 Page 20

If a, b, c are in G.P., prove that the following are also in G.P. :
a³, b³, c³

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

Therefore

b² = ac … (1)

We have to prove a³, b³, c³ are in GP or

we need to prove: (b³)² = (a³c³) {using idea of GM}

On cubing equation 1 we get,

⇒ b⁶ = a³c³

⇒ (b³)² = (a³c³)

Hence a³,b³,c³ are in GP.

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. :

a², b², c²

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 :

(a² + b²), (b² + c²), (c² + d²) are in G.P.

If a, b, c are in G.P., prove that the following are also in G.P. :a3, b3, c3