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  4. If a, b, c are in AP, then (a/bc),(1/c),(1/b) will be in

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Q. If a, b, c are in AP, then $ \frac{a}{bc},\frac{1}{c},\frac{1}{b} $ will be in

Rajasthan PETRajasthan PET 2005

Solution:

Since, a, b, c are in AP.
$ \therefore $ $ 2b=a+c $
If $ \frac{1}{bc},\frac{1}{c},\frac{1}{b} $ are in AP, then $ 2\left( \frac{1}{c} \right)=\frac{a}{bc}+\frac{1}{b} $
$ \Rightarrow $ $ \frac{2}{c}=\frac{a+c}{bc} $
$ \Rightarrow $ $ \frac{2bc}{c}=a+c $
$ \Rightarrow $ $ 2b=a+c $
Hence, $ \frac{a}{bc},\frac{1}{c},\frac{1}{b} $ are in AP.