Question

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

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

Answer 1

The correct option is A AP

$a,b,c$ are in AP
$\Rightarrow (abc+1)a,(abc+1)b,(abc+1)c$ are in AP
$\Rightarrow \frac{(abc+1)a}{abc},\frac{(abc+1)b}{abc},\frac{(abc+1)c}{abc}$ are in AP
$\Rightarrow a+\frac{1}{bc},b+\frac{1}{ac},c+\frac{1}{ab}$ are in AP
$\therefore$ Ans. is option A.