6 7 18 63 265 1365

Options

A. 1365
B. 18
C. 6
D. 265

Explanation

To solve the problem of identifying the wrong number in the series: 6, 7, 18, 63, 265, 1365, we will analyze the pattern step by step.

### Step-by-Step Solution:

1. **Identify the Pattern**:
The series appears to be generated by a combination of multiplication and addition. We will check how each number relates to the previous one.

2. **From 6 to 7**:
- \( 6 \times 1 + 1^2 = 6 + 1 = 7 \)
- This works, so we proceed to the next number.

3. **From 7 to 18**:
- \( 7 \times 2 + 2^2 = 14 + 4 = 18 \)
- This also works, so we continue.

4. **From 18 to 63**:
- \( 18 \times 3 + 3^2 = 54 + 9 = 63 \)
- This is correct, so we move to the next number.

5. **From 63 to 265**:
- We need to check if this follows the same pattern:
- \( 63 \times 4 + 4^2 = 252 + 16 = 268 \)
- Here, we find that the expected number is 268, not 265. Thus, 265 is the wrong number.

6. **From 268 to 1365**:
- To confirm the pattern continues, we check:
- \( 268 \times 5 + 5^2 = 1340 + 25 = 1365 \)
- This is correct, confirming our previous findings.

### Conclusion:
The wrong number in the series is **265**, and it should be **268**.