Discussion
The series below can be extended once the rule behind it is found. Identify the pattern, then choose the number that belongs at the question mark.
4, 16, 64, 256, ?
Answer: C
Correct answer: 1024
The gaps are 12, 48, 192, which follow no constant pattern, so the rule lies in the terms rather than in the steps between them. Each term is four raised to the power of its position: position 1 gives 4 and position 4 gives 256. The next position is 5, which gives 1024. As a check, the same rule applied to the earlier positions reproduces 4, 16, 64, 256 exactly, so it accounts for every term shown and not merely the last. Powers of three grow faster than powers of two and are recognised by the same method of trial.
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