Question

What is the sum of the first 100 natural numbers?

• A. 2200
• B. 2400
• C. 2500
• D. 2700

Answer 1

The correct option is A

2200

The formula to find the sum of n terms of an AP is
$S_n=\left(\frac{n}{2}\right)(2a+(n-1\left)d\right)$
where $S_n$ is the sum of n terms of the AP,
'n' is the number of terms,
'a' is the first term,
'd' is the common difference.
First 100 natural numbers form an AP with the first term, a = 1 and common difference, d = 1.
$\therefore$ Sum of the first 100 natural numbers = $S_{100}=\left(\frac{100}{2}\right)\left(2\right(1)+(100-1\left)1\right)$
=$\frac{100}{2}(2+99)=5050$