Directions: Find the wrong number in the series. 3, 8, 18, 46, 100, 210, 432

### Concept & Logic Analyze the pattern by looking at multiplication combined with addition/subtraction, or by looking at the differences between terms. ### Step-by-Step Solution 1. Let's test a $\times 2$ pattern, as the numbers roughly double. 2. $3 \times 2 + 2 = 8$ 3. $8 \times 2 + 2 = 18$. Let's see if this holds. 4. $18 \times 2 + 2 = 38$. The given term is $46$. This breaks the simple $+2$ pattern. 5. Let's try a different additive sequence. $3 \times 2 + 2 = 8$ $8 \times 2 + ? = 18 \Rightarrow +2$ $18 \times 2 + ? = 46 \Rightarrow +10$ $46 \times 2 + ? = 100 \Rightarrow +8$ $100 \times 2 + ? = 210 \Rightarrow +10$ $210 \times 2 + ? = 432 \Rightarrow +12$ The additions are $2, 2, 10, 8, 10, 12$. Not a clear pattern. 6. Let's try another hypothesis: Maybe the series starts differently. Let's look at the differences: $5, 10, 28, 54, 110, 222$. No obvious pattern. 7. Let's re-examine $\times 2$ with a different added sequence. What if the pattern is $\times 2 + 2$, $\times 2 + 4$, $\times 2 + 6$? $3 \times 2 + 2 = 8$ $8 \times 2 + 4 = 20$. The given term is $18$. Let's assume $18$ is wrong and should be $20$. Let's test this hypothesis forward: $20 \times 2 + 6 = 46$. Matches the next term! $46 \times 2 + 8 = 92 + 8 = 100$. Matches! $100 \times 2 + 10 = 200 + 10 = 210$. Matches! $210 \times 2 + 12 = 420 + 12 = 432$. Matches! 8. The pattern is multiplying by $2$ and adding consecutive even numbers ($2, 4, 6, 8...$). 9. The term $18$ breaks this pattern; it should be $20$. ### Exam Strategy & Shortcut If a constant addition (like $\times 2 + 2$) fails early on, try an increasing arithmetic progression for the addition (like $+2, +4, +6$). Test it on the subsequent terms to quickly confirm or reject the hypothesis. ### Common Pitfall Giving up on a base multiplier (like $\times 2$) just because the constant addition fails. Always check if the added value itself follows a sequence. ### Final Answer Therefore, the correct answer is **18**.