Discussion
The numbers below advance according to a pattern you are asked to identify. Settle on the rule the terms obey and give the next number.
36, 49, 64, 81, ?
Answer: A
Correct answer: 100
The gaps are 13, 15, 17, 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 a whole number, the numbers running consecutively: position 6 gives 36 and position 9 gives 81. The next position is 10, which gives 100. As a check, the same rule applied to the earlier positions reproduces 36, 49, 64, 81 exactly, so it accounts for every term shown and not merely the last. The position of a term in the series is as much a part of the data as its value.
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