Question

Find the sum of first 20 natural numbers.

• A. 210
• B. 220
• C. 230
• D. 240

Answer 1

The correct option is A 210

We have to find the sum n terms of the AP 1,2,3,...
Here
$a=1,d=1$.
Therefore, Required sum $S_n=\frac{n}{2}[2a+(n-1\left)d\right]=\frac{n}{2}[2\times 1+(n-1)\times 1]$
$\Rightarrow S_n=\frac{n}{2}[2+n-1]$

$\Rightarrow S_n=\frac{n(n+1)}{2}$ ...(1)

Put $n=20$ in (1), we get
$S_{20}=\frac{20(20+1)}{2}=210$