If a, b, c, d are in GP, then prove that are in GP

Question

Philoid · Accepted Answer

To prove: are in GP.

Given: a, b, c, d are in GP

Proof: When a,b,c,d are in GP then

From the above, we can have the following conclusion

⇒ bc = ad … (i)

⇒ b² = ac … (ii)

⇒ c² = bd … (iii)

Considering

=

From eqn. (i) , (ii) and (iii)

=

From the above equation, we can say that are in GP.