If each term of a G.P. is raised to the power x, show that the resulting sequence is also a G.P.

Let a, b and c be in G.P. ∴ b 2 = ac Let, b 2 = ac = m ........(i) Each term be raised to power x. So, terms = a x , b x and c x . Terms are in G.P. if common ratio between terms are equal, Since, L.H.S. = R.H.S., Hence, proved that on raising each term of a G.P. to the power x, the resulting sequence is also a G.P.