Question

the sum of the first $12$ terms of an H.P. is $\frac{1}{1200}$ and its first term and common difference is $10$, find the $8^{th}$ term.

• A. $\frac{1}{110}$
• B. $\frac{1}{220}$
• C. $\frac{1}{330}$
• D. $\frac{1}{440}$

Answer 1

The correct option is D $\frac{1}{440}$

We know the formula for sum of $n^{th}$ term in arithmetic progression.
The reciprocal of arithmetic progression is harmonic progression.
First term $=a=10$
and common difference$=d=10$
$S_n=\frac{n}{2}[2a+(n-1\left)d\right]$
$S_8=\frac{8}{2}[2\times 10+(8-1\left)10\right]$
$S_8=4[20+90]$
$S_8=440$
Sum of HP $=\frac{1}{440}$