Question

Calculate the sum of first $30$ terms of the H.P. $-2,-5,-8,-\mathrm{11....}$

• A. $\frac{2}{1365}$
• B. $\frac{-1}{1365}$
• C. $\frac{1}{1365}$
• D. $\frac{-1}{1265}$

Answer 1

Answer: (B)

$\frac{-1}{1365}$

We know the formula for sum of nth term in arithmetic progression.
The reciprocal of arithmetic progression is harmonic progression.
First term of the given arithmetic series $=-2$
The number of terms of the given A. P. series- $n=30$
We know that the sum of first n terms of the Arithmetic Progress, whose first term $=a$ and common difference $=d$ is $-3$
$S_n=\frac{n}{2}[2a+(n-1\left)d\right]$
$S_{30}=\frac{30}{2}[2\times -2+(30-1)-3]$
$S_{30}=15[-4-87]$
$S_{30}=-1365$
Sum of HP $=\frac{-1}{1365}$