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

Question

If a, b, c are in G.P., prove that the following are also in G.P. : a 3 , b 3 , c 3

Philoid · Accepted Answer

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.