Discussion
The terms shown are enough to fix the rule and so the term that follows. Find the rule and name the term that completes the run.
3, 6, 11, 18, 27, ?
Answer: C
Correct answer: 38
The gaps are 3, 5, 7, 9, which follow no constant pattern, so the rule lies in the terms rather than in the steps between them. Each term is the square of its position plus two: position 1 gives 3 and position 5 gives 27. The next position is 6, which gives 38. As a check, the same rule applied to the earlier positions reproduces 3, 6, 11, 18, 27 exactly, so it accounts for every term shown and not merely the last. A series is fully determined by its rule and its first term, so both must be identified before extending it.
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