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 2 , b 2 , c 2

Philoid · Accepted Answer

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.