Question

If a, b, c are in GP, prove that a² , b² , c² are in GP.

Answer 1

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 

\(\frac{c^2}{b^2}\) = common ratio = r 

⇒ \(\frac{c^2}{ab^2}\) [From eqn. (i)] 

⇒\(\frac{c}{a}\) = r

Considering a², b²

\(\frac{b^2}{a^2} =\) common ratio = r

\(\frac{ac}{a^2}\) [From eqn. (i)] 

⇒ \(\frac{c}{a}\) = r

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

Hence a² , b² , c² are in GP