Question

If $a,b,c$ are in HP, then $\frac{a-b}{b-c}$ is equal to

• A. $\frac{a}{b}$
• B. $\frac{b}{a}$
• C. $\frac{a}{c}$
• D. $\frac{c}{b}$

Answer 1

Answer: (C)

$\frac{a}{c}$

If $a,b,c$ are in H.P. then,
$\frac{1}{c}-\frac{1}{b}=\frac{1}{b}-\frac{1}{a}$
$\Rightarrow \frac{b-c}{c}=\frac{a-b}{a}$
$\Rightarrow \frac{a-b}{b-c}=\frac{a}{c}$
Hence, option 'C' is correct.