Question

Find the difference between the sum of first 100 natural numbers and the sum of even numbers from 1 to 100.

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

Answer 1

The correct option is C

2500

Using the formula
$S_n=\frac{n}{2}[2n+(n-1\left)d\right]$
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
Sum of even numbers from 1 to 100 = $\frac{50}{2}(2\times 2+49\times 2)$ = 2550

Hence, the difference is 5050 - 2550 = 2500