Discussion
In the following series, find the missing number.
0, 2, ?, 12, 20, 30
Answer: B
The missing number is 6.
The differences between terms are 2, 4, 6, 8, 10, rising by 2 each time:
\[ \begin{aligned} 0 + 2 &= 2 \\ 2 + 4 &= 6 \\ 6 + 6 &= 12 \\ 12 + 8 &= 20 \\ 20 + 10 &= 30 \end{aligned} \]
Equivalently, the terms are n(n - 1) for n = 1 to 6: 0, 2, 6, 12, 20, 30. 4, 8 or 10 in the gap would make the differences uneven (2, 2, 8 or 2, 6, 4 or 2, 8, 2), breaking the steady rise of 2 that the rest of the series shows.
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