Directions: Find out the wrong number in each sequence 4, 9, 19, 39, 79, 160, 319

### Concept & Logic The series follows a pattern of multiplying the previous term by 2 and then adding or subtracting a constant. Let's investigate. ### Step-by-Step Solution Let's test the relation between consecutive terms: - $4 \times 2 + 1 = 8 + 1 = 9$ - $9 \times 2 + 1 = 18 + 1 = 19$ - $19 \times 2 + 1 = 38 + 1 = 39$ - $39 \times 2 + 1 = 78 + 1 = 79$ The pattern is clearly: Next Term = (Previous Term $\times 2$) + 1. Let's apply this to find the next term: - $79 \times 2 + 1 = 158 + 1 = 159$. The given term is 160, which is incorrect. Let's verify with the next term assuming 159 is correct: - $159 \times 2 + 1 = 318 + 1 = 319$. This matches the last term. Therefore, 160 is the wrong number and should be 159. ### Exam Strategy & Shortcut When a series grows rapidly, look for multiplicative relationships. Check if the next term is close to double, triple, or square of the previous term. ### Common Pitfall Trying to find difference patterns (5, 10, 20, 40...) which works but is slightly longer than spotting the direct $\times 2 + 1$ relationship. The differences are $9-4=5$, $19-9=10$, $39-19=20$, $79-39=40$. Next difference should be $80$. So $79+80=159$. ### Final Answer Therefore, the correct answer is **160**.