Question

The arithmetic mean of $1,2,3...n$ is

• A. $\frac{n-1}{2}$
• B. $\frac{n+1}{2}$
• C. $\frac{n}{2}$
• D. $n$

Answer 1

The correct option is B

$\frac{n+1}{2}$

Correct option: (b)$\frac{n+1}{2}$

We know sum of first$n$ natural numbers,

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

Arithmetic mean of first $n$natural numbers $=\frac{(1+2+3+\dots n)}{n}$

$$\begin{gathered} =\frac{n(n+1)}{2n} \\ =\frac{(n+1)}{2} \end{gathered}$$

Hence option (b) is the answer.