Discussion
Every term here follows from the one before it, or from its own position. Settle on the rule the terms obey and give the next number.
1, 5, 17, 53, 161, ?
Answer: D
Correct answer: 485
Neither a constant difference nor a constant ratio fits, since the gaps run 4, 12, 36, 108. Each term is the previous one multiplied by 3 and then increased by 2: 1 times 3 plus 2 is 5, and 5 times 3 plus 2 is 17. Applying it once more, 161 times 3 plus 2 is 485. As a check, reversing the rule on the answer -- subtracting the constant and dividing -- returns 161, the last term shown. Two-part rules are found by asking how the differences grow rather than by how the terms grow.
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