In the number series 3, 8, 15, 24, 34, 48, 63, exactly one term is wrong. Identify the incorrect term that does not follow the underlying rule.

Introduction / Context: This is a wrong term detection problem. The series 3, 8, 15, 24, 34, 48, 63 looks irregular at first glance, but many exam series are built from simple algebraic expressions such as n^2 minus or plus a constant. By identifying such a pattern, we can see which single term breaks it.

Given Data / Assumptions:

• Given series: 3, 8, 15, 24, 34, 48, 63.
• Exactly one term is incorrect.
• The intended pattern is expected to be simple and uniform throughout the correct terms.

Concept / Approach: We suspect that each term might be related to the square of an integer minus 1. The sequence of values n^2 - 1 for n = 2, 3, 4, 5, 6, 7, 8 is very common in reasoning questions. We compare our series to this candidate pattern and see where it breaks.

Step-by-Step Solution: 1. Write n^2 - 1 for n from 2 onwards: For n = 2: 2^2 - 1 = 4 - 1 = 3 For n = 3: 3^2 - 1 = 9 - 1 = 8 For n = 4: 4^2 - 1 = 16 - 1 = 15 For n = 5: 5^2 - 1 = 25 - 1 = 24 For n = 6: 6^2 - 1 = 36 - 1 = 35 For n = 7: 7^2 - 1 = 49 - 1 = 48 For n = 8: 8^2 - 1 = 64 - 1 = 63 2. So the ideal series based on n^2 - 1 is: 3, 8, 15, 24, 35, 48, 63. 3. Now compare this ideal series with the given series: 3, 8, 15, 24, 34, 48, 63. 4. All terms match except the fifth term: it should be 35, but the given term is 34. 5. Therefore, 34 is the wrong term.

Verification / Alternative check: Reconstruct the series using the correct pattern: 3 (2^2 - 1), 8 (3^2 - 1), 15 (4^2 - 1), 24 (5^2 - 1), 35 (6^2 - 1), 48 (7^2 - 1), 63 (8^2 - 1). Every correct term can be written as n^2 - 1 for consecutive n from 2 to 8. The only mismatch in the original problem is 34, which cannot be expressed as 6^2 - 1.

Why Other Options Are Wrong:

• 15, 24, 48: Each of these numbers exactly matches the formula n^2 - 1 for some integer n, so they fit the pattern.
• For example, 24 is 5^2 - 1 and 48 is 7^2 - 1. Removing them would destroy the beautiful sequence of consecutive n^2 - 1 values.

Common Pitfalls: Candidates sometimes look only at differences between terms and see apparently irregular gaps, then guess the wrong term by intuition. However, many reasoning questions are based on simple expressions like n^2 ± 1 or n^3 ± 1. Checking these expressions would quickly reveal the correct pattern and avoid confusion.

Final Answer: The incorrect term in the series is 34.