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Question

Find the sum of first n natural numbers.


A

n(2n+1)2

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B

2n+12

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C

n(n+1)2

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D

n(2n1)2

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Solution

The correct option is C

n(n+1)2


The first n natural numbers are 1, 2, 3, 4,....., n.
This sequence forms an AP, whose first term is 1 and the common difference is 1.

The sum upto n terms of an AP is given by
Sn=n2[2a+(n1)d].

Hence, the sum of the above AP is given by

Sn=n2[(2×1)+(n1)1]

Sn=n2[1+n]

=n(n+1)2


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