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Question

If the sum of first n natural numbers is 15 times the sum of their squares, then the value of n is:


A

5

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B

6

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C

7

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D

8

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Solution

The correct option is C

7


Explanation for the correct option.

Sum of first n natural numbers =n(n+1)2

Sum of square of first n natural numbers =n(n+1)(2n+1)6

As per the given information, nn+12=15Ɨnn+12n+16

ā‡’30nn+12nn+1=2n+1ā‡’15=2n+1ā‡’2n=14ā‡’n=7

Hence, option C is correct.


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