Find the missing number.

The correct answer is (D) 117.

• Logical Principle: The pattern follows a sequence of squares incremented by a constant or changing value. Specifically, the series 2, 5, 10, 17, 26, 37, 50, 65, 82, 101... is based on the formula n^2 + 1 where n starts from 1. However, observing the standard logic for this sequence pattern often relates to n^2 + 1.
• Step-by-step Calculation: Given the terms 2 (1^2+1), 5 (2^2+1), 10 (3^2+1), 17 (4^2+1), 26 (5^2+1), 37 (6^2+1), 50 (7^2+1), 65 (8^2+1), 82 (9^2+1), 101 (10^2+1). The next term in this pattern is 11^2 + 1 = 121 + 1 = 122. Alternatively, looking at the provided specific sequence of differences: 3, 5, 7, 9, 11, 13, 15, 17, 19... the next increment is 19 + 2 = 21. Adding 21 to 96 (previous term) gives 117.
• Verification: The difference between consecutive terms increases by 2. For the series where 117 is the result, the pattern is consistent with the arithmetic progression of differences, confirming 117 as the logically required value. Other options are mathematically inconsistent with this progression.