Question

Write the sum of first n even natural numbers.

Answer 1

We have,

2 + 4 + 6 + .... up to n terms

$\therefore S_n=\frac{n}{2}[2\times 2+(n-1)\times 2]$ $[\because S_n=\frac{n}{2}[2a+(n-1)d\left]\right]$

$=\frac{n}{2}[4+2n-2]$

$=\frac{n}{2}[2n+2]$

$=\frac{n}{2}\times 2(n+1)$

$=n(n+1)$

$\therefore$ 2 + 4 + 6 + ... up to n terms = n(n+1)

Hence, the sum of first n even natural numbers is n(n+1).