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

Options

A. 14525100
B. 15415200
C. 14515200
D. 15425100

Answer

To find the missing number in the series: `1, 3, 24, 360, 8640, 302400, ?`, we can analyze the pattern of multiplication between the numbers.

### Step-by-Step Solution:

1. **Identify the pattern of multiplication:**
- 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: \( 8640 \times 35 = 302400 \)

2. **List the multipliers:**
- The multipliers are: 3, 8, 15, 24, 35.

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

4. **Continue the pattern of differences:**
- The differences between the differences are: 5, 7, 9, 11. The next difference would be \( 11 + 2 = 13 \).

5. **Calculate the next multiplier:**
- The next multiplier would be \( 35 + 13 = 48 \).

6. **Multiply the last number in the series by the next multiplier:**
- Now, we multiply \( 302400 \) by \( 48 \):
\[ 302400 \times 48 = 14515200 \]

7. **Conclusion:**
- Therefore, the number that should come in place of the question mark is **14515200**.