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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+(n−1)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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