Discussion
The numbers below advance according to a pattern you are asked to identify. Identify the pattern, then choose the number that belongs at the question mark.
3, 5, 9, 17, 33, ?
Answer: A
Correct answer: 65
The gaps are 2, 4, 8, 16, which follow no constant pattern, so the rule lies in the terms rather than in the steps between them. Each term is one more than a power of two: position 1 gives 3 and position 5 gives 33. The next position is 6, which gives 65. As a check, the same rule applied to the earlier positions reproduces 3, 5, 9, 17, 33 exactly, so it accounts for every term shown and not merely the last. Adding or subtracting one from a power of two leaves the doubling almost visible, which is how the family is spotted.
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