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)

11

Answer 2

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 $\frac{n+1}{2} = \frac{n+7}{3}$ $\Rightarrow 3n + 3 = 2n + 14$ $\Rightarrow n = 11$