1, 5, 5, 9, 7, 11, 11, 15, 12, 17

Options

A. 11
B. 12
C. 17
D. 15

Explanation

To solve the series: 1, 5, 5, 9, 7, 11, 11, 15, 12, 17, we will analyze the numbers and identify any patterns.

### Step-by-Step Solution:

1. **Identify the Pattern**:
The series appears to consist of two interleaved sequences. Let's separate the two sequences:
- Sequence 1: 1, 5, 7, 11, 12
- Sequence 2: 5, 9, 11, 15, 17

2. **Analyze Sequence 1**:
- The first sequence is: 1, 5, 7, 11, 12.
- The differences between the terms are:
- 5 - 1 = 4
- 7 - 5 = 2
- 11 - 7 = 4
- 12 - 11 = 1
- So, the pattern in this sequence seems to be alternating between adding 4 and 2, but the last term deviates from this pattern.

3. **Analyze Sequence 2**:
- The second sequence is: 5, 9, 11, 15, 17.
- The differences between the terms are:
- 9 - 5 = 4
- 11 - 9 = 2
- 15 - 11 = 4
- 17 - 15 = 2
- This sequence follows a consistent pattern of adding 4 and then 2.

4. **Identify the Error**:
- In Sequence 1, the last term should have followed the pattern of adding 2 after adding 4.
- If we add 2 to 11, we should get 13, but the series shows 12.
- Therefore, the number 12 is incorrect and should be replaced with 13.

5. **Conclusion**:
- The wrong number in the series is 12, and it should be 13.