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If a, b, c are in G.P., prove that the following are also in G.P.:
If a, b, c are in G.P., prove that the following are also in G.P.:
CBSE | Class 11 | Exercise 20.5 | Geometric Progressions | Maths | RD Sharma
If a, b, c are in G.P., prove that the following are also in G.P.:

(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.

i

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