4 6 9 13.5 20.25 30.375 ?

Options

A. 40.25
B. 45.5625
C. 42.7525
D. 48.5625

Explanation

To find the missing number in the series: 4, 6, 9, 13.5, 20.25, 30.375, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Pattern**:
- Start by examining how each term relates to the previous term.
- The first term is 4, the second term is 6.

2. **Calculate the Ratio**:
- Divide the second term by the first term:
\[ \frac{6}{4} = 1.5 \]
- This indicates that the second term is obtained by multiplying the first term by 1.5.

3. **Continue the Pattern**:
- Check the next terms:
- For the third term:
\[ 6 \times 1.5 = 9 \]
- For the fourth term:
\[ 9 \times 1.5 = 13.5 \]
- For the fifth term:
\[ 13.5 \times 1.5 = 20.25 \]
- For the sixth term:
\[ 20.25 \times 1.5 = 30.375 \]

4. **Find the Next Term**:
- Now, to find the missing number after 30.375, we multiply it by 1.5:
\[ 30.375 \times 1.5 \]
- Performing the multiplication:
\[ 30.375 \times 1.5 = 45.5625 \]

5. **Conclusion**:
- The missing number in the series is **45.5625**.

### Final Answer:
The missing number is **45.5625**.

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