For all even numbers ‘n’ f(n) is the sum of the squares of all even natural numbers less than or equal to ‘n’ If for some ‘n’ f(n) = 51 × n, what is the value of n?
For all even numbers ‘n’ f(n) is the sum of the squares of all even natural numbers less than or equal to ‘n’ If for some ‘n’ f(n) = 51 × n, what is the value of n?
Option 1 -
14
Option 2 -
16
Option 3 -
18
Option 4 -
20
Asked by Shiksha User
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1 Answer
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Correct Option - 2
Detailed Solution:Sum of square of even natural number n = 22 + 42 + 62 + ……………. +n2
= 22 [12 + 22+ 32+ ……………+ (n/2)2]
(n+1) (n+2) = 51×6
n2 + 3n +2 = 306
(n–16) (n+19) = 0
n=16
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