Latest TCS Aptitude Question SOLUTION: The ratio of sum of squares of first n natural numbers to square of sum of first n natural numbers is 17:325. the value of n is (a)15(b)25(c)35(d)30 (e)none of these

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The ratio of sum of squares of first n natural numbers to square of sum of first n natural numbers is 17:325. the value of n is (a)15(b)25(c)35(d)30 (e)none of these

Asked In TCS Ragini (13 years ago)

Solved Madhur Read Solution (6)

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Read Solution (6) :

Vatan Kumar Seth  (13 years ago)

sum of 1st n natural no.s is n(n+1)/2,

sum of sqaures of 1st n natural no.s is n(n+1)(2n+1)/6,

The ratio of sum of squares of first n natural numbers to square of sum of first n natural numbers=n(n+1)(2n+1)*2*2/(n*n*(n+1)*(n+1))
=2(2n+1)/(3n(n+1))
now by hit and trial for the given options,if we put 25 then this will give 17/325

therefore the answer is (b)25

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Madhur  (13 years ago)

sum of square of n terms =n(n+1)(2n+1)/6 -------------- eq no.1
square of sum of n terms =n^2(n+1)^2/4 ---------------eq no. 2

eq 1/2

(2n+1)2 17
------- = ----
n(n+1)3 325

only 25 satisfies this

Is this solution Helpfull? Yes (7) | No (1)  

Ayan  (13 years ago)

sum of squares of first natural numbers = n(n+1)(2n+1)/6
square of sum of first natural numbers = (n(n+1)/2)^2
thus 2(2n+1)/3n(n+1)=17/325
comparing with the solutions for n=25 only (2n+1) becomes a multiple of 17
ans is (b) 25

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rajeev  (13 years ago)

sum of square of first n natural numbers is n(n+1)(2n+1)/2
and sum of first n natural numbers is n(n+1)/2 so
the ratio of above means 2(2n+1)/n(n+1)=17/325
after solving it become 17n^2 - 1283n - 650 = 0
the above option dont satisfy it so ans is none of these

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Amrit  (13 years ago)

none of these

Is this solution Helpfull? Yes | No (5)  

Satyajit  (7 years ago)

Sum of squares of first n natural numbers is :-

= n(n+1)(2n+1)/6

Squares of sum of first n natural numbers

= (n(n+1)/2)×(n(n+1)/2).

According to the question,

=> n(n+1)(2n+1)/6:(n(n+1)/2)×(n(n+1)/2)=17:325

Thus, by solving we get n = 25.

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