# CAT 2011 | Question: 9

711 views

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. $30$

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

$S_n=\frac{n(2n+1)(2n-1)}{3}$

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

$\implies533n*3=n((2n)^2-1)$

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

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

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

$\implies 1600=4n^2$

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

$\implies n^2=400$

$\implies n=20$

Option (B) is correct.

## Related questions

1
1,446 views
The values of the numbers $2^{2004}\:\text{and}\:5^{2004}$ are written one after another. How many digits are there in all?$4008$$2003$$2004$None of these
Rajat draws a $10\times10$ grid on the ground such that there are $100$ identical squares numbered $1\:\text{to}\:100$. If he has to place two identical stones on any two...
Mohan is a carpenter who specialises in making chairs. For every assignment he undertakes, he charges his commision and cost. His commission is fixed and equals $₹560$...
$\begin{array}{}Let\;f_{n+1}(x)&=f_n(x)+1\;\text{if$n$is a multiple of 3}\\ &=f_n(x)-1\;\text{otherwise.}\end{array}$If $f_1(1)=0$, then what is $f_{50}(1)$?$-18$$-16$$... 0 votes 0 answers 5 1,328 views On a plate in the shape of an equilateral triangle$\text{ABC}$with area$16\sqrt 3\;\text{sq cm}$, a rod$\text{GD}$, of height$8\:\text{cm}\$, is fixed vertically at t...