(i) a2, b2, c2
(ii) a3, b3, c3
Solution:
(i) a2, b2, c2
According to the question, a, b, c are in GP.
Making use of the property of geometric mean, we can write:
b2 = ac
Upon squaring both the sides we get,
(b2)2 = (ac)2
(b2)2 = a2c2
∴ a2, b2, c2 are in G.P.
(ii) a3, b3, c3
According to the question, a, b, c are in GP.
Making use of the property of geometric mean, we can write:
b2 = ac
Upon squaring both the sides we get,
(b2)3 = (ac)3
(b2)3 = a3c3
(b3)2 = a3c3
∴ a3, b3, c3 are in G.P.