Question

Given that the sum of the odd integers from $1$ to $99$ inclusive is $2500$, what is the sum of the even integers from $2$ to $100$ inclusive?

• A. 2450
• B. 2550
• C. 2460
• D. 22500

Answer 1

The correct option is B 2550

Odd integers $=1,3,5,7,\mathrm{9.....}$

Sum of odd integers $=2500$

Even integers $=2,4,6,8,,\mathrm{10......}$

In the series of even integers each term is one more than the each term of odd integers.

Hence, there are $50$ terms.

So, the sum of even integers $=$ $2500+50=2550$