Question

find the sum of the first 20 even natural numbers.

• A. 400
• B. 410
• C. 420
• D. 430

Answer 1

The correct option is C 420

We have to find the sum n terms of the AP $2,4,6,...$
Here $a=2,d=4-2=2$.
Therefore, Required sum $S_n=\frac{n}{2}[2a+(n-1\left)d\right]=\frac{n}{2}[2\times 2+(n-1)\times 2]$
$\Rightarrow S_n=n[2+n-1]$
$\Rightarrow S_n=n(n+1)$ ...(1)

Put $n=20$ in (1), we get
$S_{20}=20(20+1)=420$