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 = a = 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).