Question

The sum of the first 100 natural numbers is greater than the sum of the even numbers between 1 and 100 by _____.

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

Answer 1

The correct option is C

2500

Formula for sum of n natural nmbers is $S_n=\left(\frac{n}{2}\right)(2a+(n-1\left)d\right)$
Hence, Sum of first 100 natural numbers = $\frac{100}{2}(2+99)=5050$

Sum of even numbers from 1 to 100, there are 50 even numbers between 1 and 100.

So, we have
= $\frac{50}{2}(2\times 2+49\times 2)$ = 2550.

So, the difference is 5050 - 2550 = 2500