Discussion
A rule that fits every term shown will also give the missing one. Settle on the rule the terms obey and give the next number.
1, 6, 31, 156, ?
Answer: D
Correct answer: 781
Neither a constant difference nor a constant ratio fits, since the gaps run 5, 25, 125. Each term is the previous one multiplied by 5 and then increased by 1: 1 times 5 plus 1 is 6, and 6 times 5 plus 1 is 31. Applying it once more, 156 times 5 plus 1 is 781. As a check, reversing the rule on the answer -- subtracting the constant and dividing -- returns 156, the last term shown. Substituting the answer back and regenerating the series is the only check that catches both rule and arithmetic errors.
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