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Geometric Progressions — Maths STD 11 Science — Question

Maharashtra BoardEnglish MediumSTD 11 ScienceMathsGeometric Progressions4 Marks
Question
If a, b, c, are in G.P., prove that the following are also in G.P.
$\text{a}^2,\text{b}^2,\text{c}^2$
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Answer

a, b, c are in G.P.$\Rightarrow\text{b}^2=\text{ac }\cdots{(1)}$
$\big(\text{b}^2\big)=\big(\text{ac}\big)^2$
$\big(\text{b}^2\big)^2=\text{a}^2\text{c}^2$
$\Rightarrow\text{a}^2,\text{b}^2,\text{c}^2\text{ are in G.P.}$

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