Directions: Find the wrong number in the series. 10, 26, 74, 218, 654, 1946, 5834

### Concept & Logic Analyze the rate of growth to determine the multiplier and any constant additions or subtractions. ### Step-by-Step Solution 1. The numbers are roughly tripling. Let's test a $\times 3$ relationship. 2. $10 \times 3 = 30$. To get $26$, subtract $4$. Pattern hypothesis: $\times 3 - 4$. 3. Test next term: $26 \times 3 = 78$. Subtract $4 \rightarrow 74$. Matches. 4. Next: $74 \times 3 = 222$. Subtract $4 \rightarrow 218$. Matches. 5. Next: $218 \times 3 = 654$. The formula gives $654 - 4 = 650$. The given term is $654$. This is a suspect. 6. Let's verify by using the expected term $650$ to find the next one: $650 \times 3 = 1950$. Subtract $4 \rightarrow 1946$. Matches the next term in the series! 7. The pattern is confirmed as $(previous term \times 3) - 4$. 8. The wrong number is $654$. ### Exam Strategy & Shortcut Estimate the multiplier by looking at larger terms. $1946$ to $5834$ is roughly $\times 3$ ($1900 \times 3 = 5700$). Then test the $\times 3$ hypothesis from the beginning. ### Common Pitfall Giving up on a multiplicative pattern if the direct multiple doesn't match perfectly; always remember to look for an added/subtracted constant ($ax + b$). ### Final Answer Therefore, the correct answer is **654**.