Question:
Write the sum of first n even natural numbers.
Solution:
We need to find the sum of 2, 4, 6, 8...upto n terms.
Here, a = 2, d = 2
We know:
$S_{n}=\frac{n}{2}\{2 a+(n-1) d\}$
$=\frac{n}{2}\{2 \times 2+(n-1) 2\}$
$=n(n+1)$
Therefore, the sum of the first $n$ odd numbers is $n(n+1)$.