Discussion
The terms below were produced by applying the same operation repeatedly. Determine the relationship and select the number that follows.
6, 12, 20, 30, ?
Answer: A
Correct answer: 42
The gaps are 6, 8, 10, which follow no constant pattern, so the rule lies in the terms rather than in the steps between them. Each term is the product of two consecutive whole numbers: position 1 gives 6 and position 4 gives 30. The next position is 5, which gives 42. As a check, the same rule applied to the earlier positions reproduces 6, 12, 20, 30 exactly, so it accounts for every term shown and not merely the last. Products of consecutive integers grow at roughly the same rate as squares, and the two families are easily confused.
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