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Question

# Sum of 15 consecutive positive integers is a perfect square. The smallest possible value of this sum is______

A
144
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B
169
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C
196
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D
225
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E
None of these
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Solution

## The correct option is D 225Let the 15 positive integers aren−7,n−6,n−5,n−4,n−3,n−2,n−1,n,n+1,n+2,n+3,n+4,n+5,n+6,n+7Sum is: =n−7+n−6+n−5+n−4+n−3+n−2+n−1+n+n+1+n+2+n+3+n+4+n+5+n+6+n+7=15nGiven that 15n is a perfect square∴ Smallest possible value is 15×15=225

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