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

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

Solution:

Arithmetic mean of 1, 2, 3, ... , n

$=\frac{1+2+3+\ldots+n}{n}$

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

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

Hence, the correct option is (a).