Identifying the Pattern and the Error

To find the wrong number in the series, we need to discover the mathematical rule that generates the sequence and then check which number violates that rule.

The series is: 7, 8, 18, 57, 288, 1165, 6996

The Pattern

The pattern in this series is as follows: to get the next term, you multiply the current term by a sequentially increasing number (starting with 1) and then add that same number.

The rule can be expressed as: Next Term = (Previous Term × n) + n, where n starts at 1 and increases by 1 for each step.

Verifying the Pattern

• 7 × 1 + 1 = 8 (Correct)
• 8 × 2 + 2 = 16 + 2 = 18 (Correct)
• 18 × 3 + 3 = 54 + 3 = 57 (Correct)
• 57 × 4 + 4 = 228 + 4 = 232. The series has 288 here. This is a mismatch.

Confirming the Error

Let's assume 288 is the wrong number and the correct number is 232. We can check if the rest of the series follows the pattern from this corrected value.

• Next term from 232: 232 × 5 + 5 = 1160 + 5 = 1165. This matches the next number in the series.
• Next term from 1165: 1165 × 6 + 6 = 6990 + 6 = 6996. This matches the last number in the series.

The pattern holds true for the entire sequence if we replace 288 with 232.

Conclusion

The wrong number in the series is 288.