Question

If $18HM$ 's are interted between $\frac{1}{3}$ and $\frac{1}{41}$ then value of $4^{\text{th }}HM$ is

• A. $\frac{1}{9}$
• B. $\frac{1}{11}$
• C. $\frac{1}{13}$
• D. 11

Answer 1

Answer: (B)

let $H_1,H_2,H_3,\dots .,H_{18}$ are ae $18HM$ 's between $\frac{1}{3}$ & $\frac{1}{41}$ then
$\frac{1}{H_1},\frac{1}{H_2},\frac{1}{H_3}\dots ..\frac{1}{H_{18}}\text{ are AM’s between }3\text{ and }41$
$\Rightarrow \frac{1}{H_4}=3+4\left(\frac{41-3}{19}\right)=3+8=11$
$\Rightarrow H_4=1/11$