Question

The sum of the first $100$ natural numbers is

• A. $-5050$
• B. $5005$
• C. $5050$
• D. $-5005$

Answer 1

Answer: (C)

$5050$

We know, sum of a arithmetic progression, with first term as $a$ and common difference $d$ is
$S_n=n[a+\frac{1}{2}(n-1\left)d\right]$

Here, given, $a=1$, $d=1$ and $n=100$
$S_{100}=100[1+\frac{1}{2}(100-1)1]$

$=100[1+\frac{99}{2}]$

$=100\times \frac{101}{2}$

$=5050$