Step-by-step Solution:

Correct Answer: A (13)

To find the wrong number in the series, we need to identify the pattern that connects the consecutive terms.

Step 1: Identify the Pattern

The pattern in this series is to multiply the previous number by a sequentially increasing integer (1, 2, 3, ...) and then add that same integer.

The rule is: Next Term = (Previous Term × n) + n, where n starts at 1.

Step 2: Verify the Pattern Term by Term

Let's apply this rule to the given series:

• First term: 4
• Second term: (4 × 1) + 1 = 5. (This matches the series)
• Third term: (5 × 2) + 2 = 10 + 2 = 12. The series has 13 at this position, which breaks the pattern.

Step 3: Confirm the Error

To confirm that 13 is the wrong number, let's continue the pattern using our calculated correct value of 12 and see if it generates the rest of the series correctly.

• Fourth term: (12 × 3) + 3 = 36 + 3 = 39. (This matches the series)
• Fifth term: (39 × 4) + 4 = 156 + 4 = 160. (This matches the series)
• Sixth term: (160 × 5) + 5 = 800 + 5 = 805. (This matches the series)

Conclusion

The pattern holds for the entire sequence if the third term were 12 instead of 13. Therefore, 13 is the wrong number in the given series.