Discussion
Insert the missing number 2, 6, 12, 20, 30, 42, 56, (....)
Answer: C
Each term is a product of two consecutive integers.
\[ 1 \times 2 = 2,\quad 2 \times 3 = 6,\quad 3 \times 4 = 12,\quad 4 \times 5 = 20,\quad 5 \times 6 = 30 \]
\[ 6 \times 7 = 42,\quad 7 \times 8 = 56,\quad 8 \times 9 = \mathbf{72} \]
Equivalently the differences are the even numbers 4, 6, 8, 10, 12, 14, so the next gap is 16 and \( 56 + 16 = 72 \).
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