### Step-by-Step Solution
#### Part 1: Finding the Median of the First 15 Odd Numbers
1. **List the First 15 Odd Numbers**:
The first 15 odd numbers are:
\[
1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29
\]
2. **Count the Number of Terms (n)**:
The number of terms \( n = 15 \).
3. **Identify if n is Odd or Even**:
Since \( n = 15 \) is odd, we will use the formula for the median of an odd set:
\[
\text{Median} = \text{the } \left(\frac{n + 1}{2}\right)^{th} \text{ term}
\]
4. **Calculate the Position of the Median**:
\[
\frac{n + 1}{2} = \frac{15 + 1}{2} = \frac{16}{2} = 8
\]
So, the median is the 8th term.
5. **Find the 8th Term**:
The 8th term in the list of odd numbers is \( 15 \).
6. **Conclusion**:
Therefore, the median of the first 15 odd numbers is:
\[
\text{Median} = 15
\]
#### Part 2: Finding the Median of the First 10 Even Numbers
1. **List the First 10 Even Numbers**:
The first 10 even numbers are:
\[
0, 2, 4, 6, 8, 10, 12, 14, 16, 18
\]
2. **Count the Number of Terms (n)**:
The number of terms \( n = 10 \).
3. **Identify if n is Odd or Even**:
Since \( n = 10 \) is even, we will use the formula for the median of an even set:
\[
\text{Median} = \frac{\text{the } \left(\frac{n}{2}\right)^{th} \text{ term} + \text{the } \left(\frac{n}{2} + 1\right)^{th} \text{ term}}{2}
\]
4. **Calculate the Positions of the Median**:
\[
\frac{n}{2} = \frac{10}{2} = 5 \quad \text{and} \quad \frac{n}{2} + 1 = 6
\]
So, we need the 5th and 6th terms.
5. **Find the 5th and 6th Terms**:
The 5th term is \( 8 \) and the 6th term is \( 10 \).
6. **Calculate the Median**:
\[
\text{Median} = \frac{8 + 10}{2} = \frac{18}{2} = 9
\]
7. **Conclusion**:
Therefore, the median of the first 10 even numbers is:
\[
\text{Median} = 9
\]
#### Part 3: Finding the Median of the First 50 Whole Numbers
1. **List the First 50 Whole Numbers**:
The first 50 whole numbers are:
\[
0, 1, 2, 3, 4, \ldots, 49
\]
2. **Count the Number of Terms (n)**:
The number of terms \( n = 50 \).
3. **Identify if n is Odd or Even**:
Since \( n = 50 \) is even, we will use the formula for the median of an even set:
\[
\text{Median} = \frac{\text{the } \left(\frac{n}{2}\right)^{th} \text{ term} + \text{the } \left(\frac{n}{2} + 1\right)^{th} \text{ term}}{2}
\]
4. **Calculate the Positions of the Median**:
\[
\frac{n}{2} = \frac{50}{2} = 25 \quad \text{and} \quad \frac{n}{2} + 1 = 26
\]
So, we need the 25th and 26th terms.
5. **Find the 25th and 26th Terms**:
The 25th term is \( 24 \) and the 26th term is \( 25 \).
6. **Calculate the Median**:
\[
\text{Median} = \frac{24 + 25}{2} = \frac{49}{2} = 24.5
\]
7. **Conclusion**:
Therefore, the median of the first 50 whole numbers is:
\[
\text{Median} = 24.5
\]
### Summary of Results
1. Median of the first 15 odd numbers: **15**
2. Median of the first 10 even numbers: **9**
3. Median of the first 50 whole numbers: **24.5**
