What will come in place of the question mark (?) in the following numbers ?
4 6 12 30 90 315 ?

Options

A. 945
B. 102
C. 1260
D. 1417.5

Answer

To find the number that comes in place of the question mark (?) in the sequence 4, 6, 12, 30, 90, 315, we need to identify the pattern in the sequence.

### Step-by-Step Solution:

1. **Identify the Pattern**:
- Let's analyze the sequence:
- From 4 to 6: \(4 \times \frac{3}{2} = 6\)
- From 6 to 12: \(6 \times 2 = 12\)
- From 12 to 30: \(12 \times \frac{5}{2} = 30\)
- From 30 to 90: \(30 \times 3 = 90\)
- From 90 to 315: \(90 \times \frac{7}{2} = 315\)

2. **Determine the Multiplicative Pattern**:
- The multipliers are:
- \( \frac{3}{2}, 2, \frac{5}{2}, 3, \frac{7}{2} \)
- The pattern of the multipliers appears to be increasing by \( \frac{1}{2} \) each time:
- \( \frac{3}{2} = 1.5 \)
- \( 2 = \frac{4}{2} \)
- \( \frac{5}{2} = 2.5 \)
- \( 3 = \frac{6}{2} \)
- \( \frac{7}{2} = 3.5 \)

3. **Calculate the Next Multiplier**:
- Following the identified pattern, the next multiplier should be \( 4 = \frac{8}{2} \).

4. **Calculate the Next Number**:
- Now, we multiply the last number in the sequence (315) by the next multiplier (4):
- \( 315 \times 4 = 1260 \)

5. **Conclusion**:
- Therefore, the number that comes in place of the question mark (?) is **1260**.

### Final Answer:
The answer is **1260**.