Directions: Insert the missing number: 71, 76, 69, 74, 67, 72, (....)

### Concept & Logic This is an alternating series, composed of two separate arithmetic progressions. ### Step-by-Step Solution 1. Split the series into two alternating sub-series: - Series 1 (odd positions): $71, 69, 67, \dots$ - Series 2 (even positions): $76, 74, 72, \dots$ 2. Analyze Series 1: The difference is $-2$ ($71 - 2 = 69$; $69 - 2 = 67$). 3. Analyze Series 2: The difference is also $-2$ ($76 - 2 = 74$; $74 - 2 = 72$). 4. The missing term is the next term in Series 1, which follows $67$. 5. Missing term $= 67 - 2 = 65$. ### Exam Strategy & Shortcut Alternatively, look at differences between consecutive terms: $+5, -7, +5, -7, +5, \dots$ $72 - 7 = 65$. Both methods yield the same result quickly. ### Common Pitfall Following the $+5, -7$ pattern but applying the wrong operation at the final step. ### Final Answer Therefore, the correct answer is **65**.