What wil come in the place of question mark in following number series:
1,1,?,15,105,945

Options

A. A)2
B. B)3
C. C)4
D. D)1.5

Answer

To find the missing term in the number series: 1, 1, ?, 15, 105, 945, we will analyze the pattern in the series.

### Step-by-Step Solution:

1. **Identify the given terms**: The series starts with 1, 1, ?, 15, 105, 945.

2. **Look for a pattern**: We can observe the relationship between the terms after the first two:
- The 3rd term is missing (let's denote it as K).
- The 4th term is 15.
- The 5th term is 105.
- The 6th term is 945.

3. **Calculate the ratios between consecutive terms**:
- From the 3rd term (K) to the 4th term (15):
- If we assume K is multiplied by a certain number to get 15, we can denote this multiplier as X.
- Thus, K * X = 15.
- From the 4th term (15) to the 5th term (105):
- 15 * 7 = 105 (Here, we multiplied by 7).
- From the 5th term (105) to the 6th term (945):
- 105 * 9 = 945 (Here, we multiplied by 9).

4. **Identify the multipliers**:
- The multipliers seem to follow a pattern:
- The first multiplier (from 1 to 1) is 1.
- The second multiplier (from K to 15) is 3.
- The third multiplier (from 15 to 105) is 7.
- The fourth multiplier (from 105 to 945) is 9.
- The sequence of multipliers appears to be: 1, 3, 5, 7, 9.

5. **Determine K**:
- Since we have identified that K is multiplied by 3 to yield 15, we can set up the equation:
- K * 3 = 15
- K = 15 / 3
- K = 5.

6. **Conclusion**: The missing term in the series is 5.

### Final Answer:
The missing term is **5**.