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Question

Find the sum of all odd natural numbers from 1 to 150.

A
5625
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B
5635
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C
5645
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D
5655
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Solution

The correct option is A 5625
Clearly, the odd natural numbers from 1 to 150 are 1,3,5,...,149.

This is an AP with first term a=1, common difference d=2 and last term an=l=149.

Let there be n terms in this AP.

Then,
an=149

an=a+(n1)d

149=1+(n1)×2

149=1+2n2

2n=150

n=75

required sum =Sn=n2[a+l]=752[1+149]=5625

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