Discussion
Every term here follows from the one before it, or from its own position. Identify the pattern, then choose the number that belongs at the question mark.
2, 9, 28, 65, ?
Answer: D
Correct answer: 126
The gaps are 7, 19, 37, which follow no constant pattern, so the rule lies in the terms rather than in the steps between them. Each term is the cube of its position plus one: position 1 gives 2 and position 4 gives 65. The next position is 5, which gives 126. As a check, the same rule applied to the earlier positions reproduces 2, 9, 28, 65 exactly, so it accounts for every term shown and not merely the last. Cubes grow quickly and are worth knowing to about six, beyond which the series rarely runs.
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