Discussion
The list below is incomplete by exactly one term. Settle on the rule the terms obey and give the next number.
5, 13, 29, 61, 125, ?
Answer: C
Correct answer: 253
Neither a constant difference nor a constant ratio fits, since the gaps run 8, 16, 32, 64. Each term is the previous one multiplied by 2 and then increased by 3: 5 times 2 plus 3 is 13, and 13 times 2 plus 3 is 29. Applying it once more, 125 times 2 plus 3 is 253. As a check, reversing the rule on the answer -- subtracting the constant and dividing -- returns 125, the last term shown. A series of four terms admits many rules in principle, but only one that is simple enough to be intended.
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