Question

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

Answer 1

Using the formula
$S_n=\frac{n}{2}[2a+(n-1\left)d\right]$

There are 100 natural numbers between 1 and 100. Therefore, n = 100, a = 1 and d = 1.

Sum of first 100 natural numbers = $\frac{100}{2}(2+99)=5050$

There are 50 even numbers between 1 and 100. Therefore, n = 50, a = 2 and d = 2

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