Directions: Insert the missing number: 16, 33, 65, 131, 261, (.....)

### Concept & Logic The series uses a multiplication and addition/subtraction alternating pattern. Each term is approximately double the previous one. ### Step-by-Step Solution Let's test the exact relationship by doubling the previous term: - $16 \times 2 = 32$. The actual term is 33. So, $16 \times 2 + 1 = 33$. - $33 \times 2 = 66$. The actual term is 65. So, $33 \times 2 - 1 = 65$. - $65 \times 2 = 130$. The actual term is 131. So, $65 \times 2 + 1 = 131$. - $131 \times 2 = 262$. The actual term is 261. So, $131 \times 2 - 1 = 261$. The pattern is alternating: $\times 2 + 1$, $\times 2 - 1$, $\times 2 + 1$, $\times 2 - 1$. The last operation applied was $\times 2 - 1$. Therefore, the next operation to find the missing number must be $\times 2 + 1$. $261 \times 2 + 1 = 522 + 1 = 523$. ### Exam Strategy & Shortcut When numbers roughly double at each step, multiply by 2 and observe the residual difference. An alternating $+1, -1$ pattern will quickly reveal itself. ### Common Pitfall Losing track of the alternation and accidentally applying $-1$ instead of $+1$ for the final step, leading to the incorrect answer 521. ### Final Answer Therefore, the correct answer is **523**.