Discussion
Find the missing number.
2, 6, 12, 20, 30, ?
Answer: C
The missing number is 42.
Each term is the product of two consecutive whole numbers:
\[ \begin{aligned} &1\times2,\ 2\times3,\ 3\times4, \\ &4\times5,\ 5\times6,\ 6\times7 \end{aligned} \]
which gives 2, 6, 12, 20, 30 and then 42. Equivalently, the differences rise by 2 each time: 4, 6, 8, 10, so the next difference is 12, and 30 + 12 = 42.
36 and 40 add too little (6 and 10) and 44 too much (14), so they break the pattern.
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