Question

The sum of third and ninth term of an H.P is $\frac{1}{8}$. Find the sum of the first $11$ terms of the progression.

Answer 1

The third term $t_3=a+3d$
The ninth term $t_9=a+8d$
$t_3+t_9=2a+10d=8$
Sum of first $11$ terms of an AP is given by
$S_{1}1=\frac{n}{2}[2a+10d]$
$S_{1}1=\frac{11}{2}\times 8=44$
The reciprocal of arithmetic progression is harmonic progression.
So, Sum of HP $=\frac{1}{44}$