2 8 12 20 30 42 56

Options

A. 8
B. 42
C. 30
D. 20

Explanation

To find the wrong number in the series 2, 8, 12, 20, 30, 42, 56, we will analyze the differences between consecutive terms and identify any inconsistencies.

### Step-by-Step Solution:

1. **List the series**:
The series given is:
\[ 2, 8, 12, 20, 30, 42, 56 \]

2. **Calculate the differences between consecutive terms**:
- \(8 - 2 = 6\)
- \(12 - 8 = 4\)
- \(20 - 12 = 8\)
- \(30 - 20 = 10\)
- \(42 - 30 = 12\)
- \(56 - 42 = 14\)

So, the differences are:
\[ 6, 4, 8, 10, 12, 14 \]

3. **List the differences**:
The differences we calculated are:
- First difference: 6
- Second difference: 4
- Third difference: 8
- Fourth difference: 10
- Fifth difference: 12
- Sixth difference: 14

4. **Analyze the pattern of differences**:
The differences seem to follow a pattern, but they are not consistent. Let's look at the expected pattern:
- The differences should ideally increase by 2 each time starting from 6:
- Expected differences: 6, 8, 10, 12, 14, 16

5. **Identify the inconsistency**:
- The second difference is 4, which does not fit the expected pattern.
- If we replace 8 with a number that fits the pattern, we can check what that number should be.
- If we assume the second number should be 6 (to maintain the pattern), then:
- The series would be: \(2, 6, 12, 20, 30, 42, 56\)

6. **Check the new series**:
- New differences:
- \(6 - 2 = 4\)
- \(12 - 6 = 6\)
- \(20 - 12 = 8\)
- \(30 - 20 = 10\)
- \(42 - 30 = 12\)
- \(56 - 42 = 14\)

This gives us:
\[ 4, 6, 8, 10, 12, 14 \]
which follows the expected pattern of increasing by 2.

7. **Conclusion**:
The number that does not fit the pattern is **8**. Therefore, the wrong number in the series is **8**.