Discussion
The numbers below are not random; a rule accounts for all of them. Settle on the rule the terms obey and give the next number.
3, 10, 24, 52, 108, ?
Answer: A
Correct answer: 220
Neither a constant difference nor a constant ratio fits, since the gaps run 7, 14, 28, 56. Each term is the previous one multiplied by 2 and then increased by 4: 3 times 2 plus 4 is 10, and 10 times 2 plus 4 is 24. Applying it once more, 108 times 2 plus 4 is 220. As a check, reversing the rule on the answer -- subtracting the constant and dividing -- returns 108, the last term shown. Testing a candidate rule against the first pair as well as the last is what exposes a rule that happens to fit only the recent terms.
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