Question

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

• A. AP
• B. GP
• C. HP
• D. None of these

Answer 1

Answer: (A)

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.