Complete the series : 2, 5, 9, 19, 37, .....

### Concept & Logic The series follows a pattern of multiplying the previous term by $2$ and then alternately adding or subtracting a number. Let's check the differences. ### Step-by-Step Solution 1. Analyze the relationship between consecutive terms: - $2 \times 2 + 1 = 5$ - $5 \times 2 - 1 = 9$ - $9 \times 2 + 1 = 19$ - $19 \times 2 - 1 = 37$ 2. The pattern is $\times 2 + 1$, $\times 2 - 1$, $\times 2 + 1$, $\times 2 - 1, \dots$ 3. The next operation should be $\times 2 + 1$. 4. Next term $= 37 \times 2 + 1 = 74 + 1 = 75$. ### Exam Strategy & Shortcut Whenever a series roughly doubles at each step, check the relation $y = 2x \pm c$. Here, it alternates between $+1$ and $-1$. ### Common Pitfall Missing the alternating $+1, -1$ and simply doubling and subtracting $1$ every time, or adding $1$ every time. ### Final Answer Therefore, the correct answer is **75**.