Discussion
The missing number in the sequence 2, 6, 12, ______, 30 is
Answer: C
The missing number is 20.
Each term is the product of two consecutive numbers:
\[ \begin{aligned} &1 \times 2,\ 2 \times 3,\ 3 \times 4, \\ &4 \times 5,\ 5 \times 6 \end{aligned} \]
which gives 2, 6, 12, 20, 30. Equivalently, the differences grow by 2 each time: 4, 6, 8, 10, so the gap after 12 must be 8 and the gap before 30 must be 10. Each wrong option breaks this: 15 would leave gaps of 3 and 15, 18 gaps of 6 and 12, and 25 gaps of 13 and 5.
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