Insert one arithmetic mean between 3 and 13.

Answer

To find one arithmetic mean between 3 and 13, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the two numbers**: We are given the numbers 3 and 13.

2. **Use the formula for the arithmetic mean**: The formula for finding the arithmetic mean (AM) between two numbers \( a \) and \( b \) is:
\[ AM = \frac{a + b}{2} \]

3. **Substitute the values into the formula**: Here, \( a = 3 \) and \( b = 13 \). So we substitute these values into the formula:
\[ AM = \frac{3 + 13}{2} \]

4. **Calculate the sum of the numbers**: First, we calculate the sum of 3 and 13:
\[ 3 + 13 = 16 \]

5. **Divide the sum by 2**: Now, we divide the sum by 2 to find the arithmetic mean:
\[ AM = \frac{16}{2} = 8 \]

6. **State the final answer**: Therefore, the arithmetic mean between 3 and 13 is:
\[ \text{AM} = 8 \]

### Final Answer:
The required arithmetic mean is **8**.

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