Question

Find the sum of first n even natural numbers.

Answer 1

Even numbers: 2,4,6,....

a = 2,

d= 2

Sum of n terms, $S_n=\frac{n}{2}[2a+(n-1\left)d\right]=\frac{n}{2}\left[2\right(2)+(n-1\left)2\right]=\frac{n}{2}[4+2n-2]=\frac{n}{2}[2n+2]=n(n+1)$

Sum of n even numbers , $S_n=n(n+1)$