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Question

The sum of 18 consecutive natural numbers is a perfect square. What is the smallest possible value of this sum?

A
169
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B
225
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C
289
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D
441
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Solution

The correct option is A 225
Let the numbers be
a,a+1,a+2,.....a+17
This is an A.P with
First term =a
Common difference d=1
Terms n=18
Sum of the terms
Sn==182(2a+17)
=9(2a+17)
=18a+153
For a=1,Sn=171
a=1,Sn=189
a=3,Sn=207
a=4,Sn=225
=152 (A perfect square)

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