If a, b, c are in GP, prove that a 2 , b 2 , c 2 are in GP.

Question

Philoid · Accepted Answer

To prove: a², b², c² are in GP

Given: a, b, c are in GP

Proof: As a, b, c are in GP

⇒ b² = ac … (i)

Considering b², c²

= common ratio = r

⇒ [From eqn. (i)]

⇒ = r

Considering a², b²

= common ratio = r

⇒ [From eqn. (i)]

⇒ = r

We can see that in both the cases we have obtained a common ratio.

Hence a², b², c² are in GP.