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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.

The arithmetic mean of the first n natural numbers is?

Understand how to calculate the arithmetic mean of the first n natural numbers using the formula M = (n+1)/2. Learn the steps to derive this formula and solve related problems, suitable for students in Grades 6-8.

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