Question

If $a,b,c$ are in AP; then $\frac{1}{bc},\frac{1}{ca}and\frac{1}{ab}$ are in AP.

• A. True
• B. False

Answer 1

The correct option is A

True

If $a,b,c$ are in AP, then a +c = 2b .... (i)

To check if $\frac{1}{bc},\frac{1}{ca}and\frac{1}{ab}$ are in AP,

$\frac{1}{bc}+\frac{1}{ab}=\frac{a+c}{abc}$
$=\frac{2b}{abc}$
$=\frac{2}{ac}$

Hence proved.

So the statement is true