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Question
If a, b, c are in G.P., prove that the following is also in G.P.:
a3, b3, c3
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Solution
a, b and c are in G.P.
∴ \[b^2 = ac . . . . . . . (1)\]
\[\left( b^3 \right)^2 = \left( b^2 \right)^3 = \left( ac \right)^3 \left[\text { Using } (1) \right]\]
\[ \Rightarrow \left( b^3 \right)^2 = a^3 c^3 \]
\[\text { Therefore }, a^3 , b^3 \text { and } c^3 \text { are also in G . P } .\]
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