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