Directions: Find the wrong number in the series. 2, 3, 6, 15, 52.5, 157.5, 630

### Concept & Logic The sudden appearance of $.5$ decimals strongly suggests that the terms are being multiplied by fractions or decimals, typically increasing by $0.5$. ### Step-by-Step Solution 1. Examine the ratios between consecutive terms. 2. $3 / 2 = 1.5$ 3. $6 / 3 = 2$ 4. $15 / 6 = 2.5$ 5. The multipliers are forming a clear sequence: $\times 1.5, \times 2, \times 2.5$. 6. The next multiplier should be $\times 3$. 7. $15 \times 3 = 45$. The given term in the series is $52.5$. This is highly suspect. 8. Let's test if the expected term $45$ restores the rest of the pattern. The next multiplier should be $\times 3.5$. 9. $45 \times 3.5 = 157.5$. Matches the next term perfectly! 10. Verify the final term with the next multiplier, $\times 4$. 11. $157.5 \times 4 = 630$. Matches the final term perfectly! 12. The pattern of increasing decimal multipliers is confirmed. The wrong number is $52.5$. ### Exam Strategy & Shortcut When you see $0.5$ in a sequence that is growing, immediately write out the ratios of the first few integers to find the decimal multiplier sequence ($\times 1.5, \times 2, \times 2.5$). ### Common Pitfall Trying to find an additive pattern for the first few integer terms, which completely falls apart once the decimals appear. ### Final Answer Therefore, the correct answer is **52.5**.