Question

If the mean of $n$ observations $1^3,2^3,3^3\cdots n^{3}is\frac{7{(n+1)}^2}{4},$ then the value of $n$ equals

• A. $4$
• B. $5$
• C. $6$
• D. $7$

Answer 1

The correct option is D $7$

We have, mean $=\frac{1^3+2^3+4^3+............+n^3}{n}=\frac{\sum n^3}{n}=\frac{7(n+1{)}^2}{4}$, (given)
$\Rightarrow \frac{n(n+1{)}^2}{4}=\frac{7(n+1{)}^2}{4}\Rightarrow n=7$