3, ?, 14, 55, 274, 1643

Options

A. 11
B. 5
C. 6
D. 8

Explanation

To find the missing number in the series: 3, ?, 14, 55, 274, 1643, we need to identify the pattern in the series.

### Step-by-Step Solution:

1. **Identify the Known Numbers**: The series we have is 3, ?, 14, 55, 274, 1643.

2. **Look for a Pattern**: We can see that the numbers are increasing significantly. This suggests that there might be a multiplication pattern involved.

3. **Analyze the Known Numbers**:
- From 14 to 55:
- \( 14 \times 4 - 1 = 55 \)
- From 55 to 274:
- \( 55 \times 5 - 1 = 274 \)
- From 274 to 1643:
- \( 274 \times 6 - 1 = 1643 \)

4. **Establish the Multiplication Pattern**:
- The pattern seems to be that each number is multiplied by an increasing integer (4, 5, 6, ...) and then 1 is subtracted from the result.

5. **Find the Missing Number**:
- To find the number before 14, we can work backwards:
- Let the missing number be \( x \).
- We know that \( x \times 3 - 1 = 14 \).
- Rearranging gives us \( x \times 3 = 15 \).
- Therefore, \( x = \frac{15}{3} = 5 \).

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

### Final Series:
The complete series is: 3, 5, 14, 55, 274, 1643.