Discussion
Every term here follows from the one before it, or from its own position. Determine the relationship and select the number that follows.
3, 6, 11, 20, 37, ?
Answer: D
Correct answer: 70
The gaps are 3, 5, 9, 17, which follow no constant pattern, so the rule lies in the terms rather than in the steps between them. Each term is a power of two plus the position itself: position 1 gives 3 and position 5 gives 37. The next position is 6, which gives 70. As a check, the same rule applied to the earlier positions reproduces 3, 6, 11, 20, 37 exactly, so it accounts for every term shown and not merely the last. Series built on position number formulas can be extended to any position without computing the intervening terms.
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