Discussion
The sequence below breaks off before its final term. Determine the relationship and select the number that follows.
2, 4, 8, 16, 32, 64, ?
Answer: C
Correct answer: 128
The gaps are 2, 4, 8, 16, 32, which follow no constant pattern, so the rule lies in the terms rather than in the steps between them. Each term is two raised to the power of its position: position 1 gives 2 and position 6 gives 64. The next position is 7, which gives 128. As a check, the same rule applied to the earlier positions reproduces 2, 4, 8, 16, 32, 64 exactly, so it accounts for every term shown and not merely the last. Factorials grow faster than any power, which is usually the clue that the multiplier is itself increasing.
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