Discussion
The run below is governed by one rule from beginning to end. Identify the pattern, then choose the number that belongs at the question mark.
2, 5, 10, 17, 26, ?
Answer: C
Correct answer: 37
The gaps are 3, 5, 7, 9, which follow no constant pattern, so the rule lies in the terms rather than in the steps between them. Each term is the square of its position plus one: position 1 gives 2 and position 5 gives 26. The next position is 6, which gives 37. As a check, the same rule applied to the earlier positions reproduces 2, 5, 10, 17, 26 exactly, so it accounts for every term shown and not merely the last. Perfect squares are worth recognising on sight up to about twenty, since they appear throughout this topic.
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