? 30 105 472.5 2598.75 16891.875

Options

A. 24
B. 10
C. 12
D. 16

Explanation

To solve the series: ? 30 105 472.5 2598.75 16891.875, we need to identify the pattern in the numbers provided.

### Step-by-Step Solution:

1. **Identify the Known Values**:
The series we have is: ?, 30, 105, 472.5, 2598.75, 16891.875.

2. **Calculate Ratios Between Consecutive Terms**:
- First, we calculate the ratio of 105 to 30:
\[ \frac{105}{30} = 3.5 \]
- Next, we calculate the ratio of 472.5 to 105:
\[ \frac{472.5}{105} = 4.5 \]
- Then, we calculate the ratio of 2598.75 to 472.5:
\[ \frac{2598.75}{472.5} = 5.5 \]
- Finally, we calculate the ratio of 16891.875 to 2598.75:
\[ \frac{16891.875}{2598.75} = 6.5 \]

3. **Identify the Pattern in Ratios**:
The ratios calculated are:
- 3.5
- 4.5
- 5.5
- 6.5
We can see that the ratios are increasing by 1 each time.

4. **Determine the Missing Value**:
To find the missing value (let's call it X), we assume that the ratio before 3.5 should be 2.5 (since the pattern is decreasing by 1).
Therefore, we can set up the equation:
\[ \frac{30}{X} = 2.5 \]

5. **Solve for X**:
Rearranging the equation gives:
\[ X = \frac{30}{2.5} \]
Now, performing the division:
\[ X = 12 \]

6. **Final Series**:
The completed series is: 12, 30, 105, 472.5, 2598.75, 16891.875.

### Conclusion:
The missing number in the series is **12**.