Question

If the mean of first n natural numbers is equal to $\frac{n+7}{3}$, then n is equal to

• A. 10
• B. 11
• C. 12
• D. none of these.

Answer 1

Answer: (B)

Since, the mean of first n natural numbers is $\frac{\sum n}{n}=\frac{n\left(n+1\right)}{2n}=\frac{n+1}{2},$ therefore, we must have
$\frac{n+1}{2}=\frac{n+7}{3}$
$\Rightarrow 3n+3=2n+14$
$\Rightarrow n=11$