What should come in place of the question mark (?) in the following number series?
1 3 24 360 8640 302400 ?

Options

A. 14525100
B. 154152000
C. 14515200
D. 15425100

Answer

To find the next term in the series: 1, 3, 24, 360, 8640, 302400, ?, we will analyze the pattern of multiplication between the terms.

### Step-by-Step Solution:

1. **Identify the series**:
The series is: 1, 3, 24, 360, 8640, 302400.

2. **Find the multiplication factors**:
- From 1 to 3:
\[ 1 \times 3 = 3 \]
- From 3 to 24:
\[ 3 \times 8 = 24 \]
- From 24 to 360:
\[ 24 \times 15 = 360 \]
- From 360 to 8640:
\[ 360 \times 24 = 8640 \]
- From 8640 to 302400:
\[ 8640 \times 35 = 302400 \]

3. **Identify the pattern in the multiplication factors**:
The multiplication factors are: 3, 8, 15, 24, 35.
- The differences between these factors are:
- \(8 - 3 = 5\)
- \(15 - 8 = 7\)
- \(24 - 15 = 9\)
- \(35 - 24 = 11\)

The differences (5, 7, 9, 11) indicate that we are adding consecutive odd numbers (2, 2, 2, 2).

4. **Predict the next multiplication factor**:
The next difference after 11 would be 13 (continuing the pattern of adding 2).
Thus, the next multiplication factor would be:
\[ 35 + 13 = 48 \]

5. **Calculate the next term**:
Now, we will multiply the last term in the series (302400) by the next multiplication factor (48):
\[ 302400 \times 48 \]

Performing the multiplication:
\[ 302400 \times 48 = 14515200 \]

6. **Conclusion**:
The next term in the series is:
\[ 14515200 \]

### Final Answer:
14515200