1. The problem is to find the missing number in the series: __ 85 81 83 79 81 77. 2. Observe the pattern by looking at the differences between consecutive numbers: - From 85 to 81: $85 - 81 = 4$ - From 81 to 83: $83 - 81 = 2$ - From 83 to 79: $83 - 79 = 4$ - From 79 to 81: $81 - 79 = 2$ - From 81 to 77: $81 - 77 = 4$ 3. The differences alternate between 4 and 2, decreasing the number by 4, then increasing by 2, then decreasing by 4, and so on. 4. Since the first known number is 85 and the next is 81 (a decrease of 4), the missing number before 85 should be found by reversing the pattern. 5. Before 85, the difference should be +2 (since the pattern alternates 4, 2, 4, 2,...), so the missing number is $85 + 2 = 87$. 6. Therefore, the complete series is: 87 85 81 83 79 81 77. 7. The missing number is $\boxed{87}$.