Question

If $a, b, c$ are in $HP,$ then $\frac{a}{b+c}, \frac{b}{c+a}, \frac{c}{a+b}$ will be in

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

Answer 1

Answer: (C)

$HP$

Answer 2

$a, b, c$ are in $HP$
$\Rightarrow \frac{1}{a}, \frac{1}{b}, \frac{1}{c}$ are in $AP.$
$\Rightarrow \frac{a+b+c}{a}, \frac{a+b+c}{b}, \frac{a+b+c}{c}$ are in $AP.$
$\Rightarrow 1+\frac{b+c}{a}, 1+\frac{a+c}{b}, 1+\frac{a+b}{c}$ are in $AP.$
$\Rightarrow \frac{b+c}{a}, \frac{a+c}{b}, \frac{a+b}{c}$ are in $AP.$
$\Rightarrow \frac{a}{b+c}, \frac{b}{c+a}, \frac{c}{a+b}$are in $HP.$