Directions: Find the wrong number in the series. 3, 8, 15, 24, 34, 48, 63

### Concept & Logic The series follows a pattern of squares of consecutive integers minus $1$. Let's verify this. ### Step-by-Step Solution 1. Check the pattern of squares: - $2^2 - 1 = 4 - 1 = 3$ - $3^2 - 1 = 9 - 1 = 8$ - $4^2 - 1 = 16 - 1 = 15$ - $5^2 - 1 = 25 - 1 = 24$ - $6^2 - 1 = 36 - 1 = 35$ (Wait, the given number is 34) - $7^2 - 1 = 49 - 1 = 48$ - $8^2 - 1 = 64 - 1 = 63$ 2. Alternatively, check the differences: - $8 - 3 = 5$ - $15 - 8 = 7$ - $24 - 15 = 9$ - The differences are consecutive odd numbers: $5, 7, 9, 11, 13, 15$. - Next term should be $24 + 11 = 35$. The given term is $34$. - The term after that would be $35 + 13 = 48$, which is correct. 3. Therefore, $34$ is the wrong number in the series. It should be $35$. ### Exam Strategy & Shortcut Familiarity with squares and numbers near squares ($n^2-1, n^2+1$) is crucial for solving series questions quickly. ### Common Pitfall Not checking the term *after* the suspected wrong number to confirm the pattern holds. Always verify that replacing the wrong number fixes the rest of the sequence. ### Final Answer Therefore, the correct answer is **34**.