in Quantitative Aptitude edited by
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Let $\text{S}_n$ denote the sum of the squares of the first $n$ odd natural numbers. If $\text{S}_n=533n,$ find the value of $n$.

  1. $18$
  2. $20$
  3. $24$
  4. $30$
in Quantitative Aptitude edited by
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1 Answer

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The sum of the squares  of the first n odd natural number is given by;


It is given that $S_n=533n$ so;


$\implies 1599*n=4n^3-n$

$\implies 1599*n=n(4n^2-1)$

$\implies 1599+1=4n^2$

$\implies 1600=4n^2$

$\implies n^2=\frac{1600}{4}$

$\implies n^2=400$

$\implies n=20$

Option (B) is correct.
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