9 4.5 4.5 6.75 13.5 33.75 ?

Options

A. 101.25
B. 103.75
C. 99.75
D. 105.5

Explanation

To find the missing number in the series: 9, 4.5, 4.5, 6.75, 13.5, 33.75, ?, we can analyze the pattern of multiplication between the numbers.

### Step-by-Step Solution:

1. **Identify the first term and the operation**:
- The first term is **9**.
- To get from **9** to **4.5**, we can see that:
\[ 9 \times 0.5 = 4.5 \]

2. **Identify the second term**:
- The second term is **4.5**.
- To get from **4.5** to the next **4.5**, we multiply by:
\[ 4.5 \times 1 = 4.5 \]

3. **Identify the third term**:
- The next term is **6.75**.
- To get from **4.5** to **6.75**, we multiply by:
\[ 4.5 \times 1.5 = 6.75 \]

4. **Identify the fourth term**:
- The next term is **13.5**.
- To get from **6.75** to **13.5**, we multiply by:
\[ 6.75 \times 2 = 13.5 \]

5. **Identify the fifth term**:
- The next term is **33.75**.
- To get from **13.5** to **33.75**, we multiply by:
\[ 13.5 \times 2.5 = 33.75 \]

6. **Identify the missing term**:
- Now, to find the next term after **33.75**, we will multiply by:
\[ 33.75 \times 3 = 101.25 \]

### Conclusion:
The missing number in the series is **101.25**.