The question asks for the arithmetic mean of the first $n$ natural numbers. The formula for the sum of the first $n$ natural numbers is:

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

To find the arithmetic mean, we divide this sum by the total number of terms, which is $n$. So the arithmetic mean $M$ is:

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

Thus, the correct option is:

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

Would you like more details on this? Here are 5 related questions:

1. How do you derive the formula for the sum of the first $n$ natural numbers?
2. What is the arithmetic mean of the first 100 natural numbers?
3. How does the arithmetic mean of the first $n$ even numbers differ from this?
4. Can this formula be used to find the mean of non-consecutive sequences?
5. How would you generalize this for sequences other than natural numbers?

Tip: The formula for the arithmetic mean of any sequence is the sum of the terms divided by the number of terms.