Discussion
The run of numbers below stops one term short of where it should. Settle on the rule the terms obey and give the next number.
125, 216, 343, 512, ?
Answer: A
Correct answer: 729
The gaps are 91, 127, 169, which follow no constant pattern, so the rule lies in the terms rather than in the steps between them. Each term is the cube of a whole number, the numbers running consecutively: position 5 gives 125 and position 8 gives 512. The next position is 9, which gives 729. As a check, the same rule applied to the earlier positions reproduces 125, 216, 343, 512 exactly, so it accounts for every term shown and not merely the last. Where the terms are all multiples of a common number, dividing through often simplifies the pattern.
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