Question

Sum of the first $20$ odd natural numbers is

• A. $400$
• B. $40$
• C. $200$
• D. $0$

Answer 1

Answer: (A)

$400$

An odd number is one that is not divisible by $2$ and the first odd natural number is $1.$ Since two consecutive odd numbers differ by two, the first $20$ odd natural numbers are

$1,3,5,7,9,11,13,15,17,19,21,23,25,27,29,31,33,35,37,39$

which is an A.P. with the first term $a=1,$ the common difference $d=2$and total number of terms $n=20.$ Applying the general formula for the sum of an A.P.

$S_n=\frac{n}{2}\left[2a+(n–1)d\right]$

$\Rightarrow S_{20}=\frac{20}{2}\left[2\right(1)+(20-1\left)\right(2\left)\right]$

$\Rightarrow S_{20}=10(2+38)$

$\Rightarrow S_{20}=400$