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Question

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


A

2200

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B

2400

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C

2500

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D

2700

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Solution

The correct option is C

2500


Using the formula
Sn=n2[2a+(n1)d]

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

Sum of first 100 natural numbers = 1002(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 = 502(2×2+49×2) = 2550

Hence, the difference is 5050 - 2550 = 2500


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