The sequence can be analyzed by separating it into two alternating subsequences based on position.
Odd positions (1st, 3rd, 5th, 7th, ...):
71, 74, 77, 80
The differences are:
74 - 71 = 3
77 - 74 = 3
80 - 77 = 3
Pattern: Each term increases by 3
Even positions (2nd, 4th, 6th, 8th, ...):
81, 77, 73, 69
The differences are:
77 - 81 = -4
73 - 77 = -4
69 - 73 = -4
Pattern: Each term decreases by 4
For the next four terms (positions 9, 10, 11, 12):
Position 9 (odd): 80+3=83
Position 10 (even): 69−4=65
Position 11 (odd): 83+3=86
Position 12 (even): 65−4=61
The sequence continues as: 83, 65, 86, 61
Matching with given options:
- (A) = 65
- (B) = 86
- (C) = 61
- (D) = 83
The order is: (D), (A), (B), (C)
Therefore, the answer is Option 2.