To prove: \(\frac{1}{(a^2 + b^2)}, \frac{1}{(b^2 + c^2)}, \frac{1}{(c^2 + d^2)}\) are in GP.
Given: a, b, c, d are in GP
Proof: When a, b, c, d are in GP then
\(\Rightarrow\) \(\frac{b}{a} = \frac{c}{b} = \frac{d}{c}\)
From the above, we can have the following conclusion
⇒ bc = ad … (i)
⇒ b2 = ac … (ii)
⇒ c2 = bd … (iii)
From eqn. (i) , (ii) and (iii)
From the above equation, we can say that \(\frac{1}{(a^2 + b^2)}, \frac{1}{(b^2 + c^2)}, \frac{1}{(c^2 + d^2)}\) are in GP.