Discussion
The terms below were produced by applying the same operation repeatedly. Identify the pattern, then choose the number that belongs at the question mark.
2, 6, 12, 20, 30, ?
Answer: A
Correct answer: 42
The gaps are 4, 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 square of its position plus the position itself: position 2 gives 2 and position 6 gives 30. The next position is 7, which gives 42. As a check, the same rule applied to the earlier positions reproduces 2, 6, 12, 20, 30 exactly, so it accounts for every term shown and not merely the last. A square series grows faster than any arithmetic one but more slowly than a geometric one, which places it at a glance.
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