Discussion
The sequence below breaks off before its final term. Settle on the rule the terms obey and give the next number.
2, 5, 11, 23, 47, ?
Answer: C
Correct answer: 95
Neither a constant difference nor a constant ratio fits, since the gaps run 3, 6, 12, 24. Each term is the previous one multiplied by 2 and then increased by 1: 2 times 2 plus 1 is 5, and 5 times 2 plus 1 is 11. Applying it once more, 47 times 2 plus 1 is 95. As a check, reversing the rule on the answer -- subtracting the constant and dividing -- returns 47, the last term shown. A rule that multiplies and then adds produces differences that themselves grow geometrically, which is how the family is identified.
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