Discussion
The run below is governed by one rule from beginning to end. Determine the relationship and select the number that follows.
2, 8, 18, 32, 50, ?
Answer: C
Correct answer: 72
The gaps are 6, 10, 14, 18, which follow no constant pattern, so the rule lies in the terms rather than in the steps between them. Each term is twice the square of its position: position 1 gives 2 and position 5 gives 50. The next position is 6, which gives 72. As a check, the same rule applied to the earlier positions reproduces 2, 8, 18, 32, 50 exactly, so it accounts for every term shown and not merely the last. Where the gaps alternate, the series advances by their sum every two terms, which is a quick way to jump ahead.
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