What will come in place of question mark (?) in the following sereis questions?
12,30,56,90,?,182

Options

A. A)121
B. B)132
C. C)144
D. D)156

Answer

To solve the series 12, 30, 56, 90, ?, 182, we will look for a pattern in the numbers given.

### Step-by-Step Solution:

1. **Identify the terms in the series**: The series is 12, 30, 56, 90, ?, 182.

2. **Express each term in the series as a product of two consecutive integers**:
- The first term (12) can be expressed as \(3 \times 4\).
- The second term (30) can be expressed as \(5 \times 6\).
- The third term (56) can be expressed as \(7 \times 8\).
- The fourth term (90) can be expressed as \(9 \times 10\).
- The last term (182) can be expressed as \(13 \times 14\).

3. **Recognize the pattern**: The pattern shows that each term can be represented as \(n \times (n + 1)\), where \(n\) takes on the values 3, 5, 7, 9, and 13 for the respective terms.

4. **Determine the missing term**:
- The sequence of \(n\) values is: 3, 5, 7, 9, ?, 13.
- The missing \(n\) value between 9 and 13 is 11.
- Therefore, the missing term can be calculated as:
\[ K = 11 \times 12 = 132 \]

5. **Conclusion**: The missing term in the series is 132.

### Final Answer:
The value that comes in place of the question mark (?) is **132**.