smc

The sum of the first $n$ positive integers is the same as the nth triangular number, which can be expressed as $\frac{(n)(n+1)}{2}$. Since the question is asking for the arithmetic mean, the whole sum is divided by $n$, thus giving us $\frac{\frac{(n)(n+1)}{2}}{n}$, which then simplifies to $\boxed{\frac{n+1}{2}}$.