# The sum of first 20 odd natural numbers is

Question:

The sum of first 20 odd natural numbers is

(a) 100

(b) 210

(c) 400

(d) 420

Solution:

Let a be the first term and d be the common difference.

We know that, sum of first $n$ terms $=S_{n}=\frac{n}{2}[2 a+(n-1) d]$

The given series is 1 + 3 + 5 + ......

First term = =  1.

Common difference = d = 3 − 1 = 2

$\therefore S_{20}=\frac{20}{2}[2 \times 1+(20-1) 2]$

$=10(2+19 \times 2)$

$=10(40)$

$=400$

Hence, the correct option is (c).