Discussion
Find out the missing term in the following series
1, 1, 2, 6, 24, ?, 720.
Answer: B
The missing term is 120.
Each term is the previous term multiplied by the next counting number, so the terms are factorials:
\[ \begin{aligned} &1,\ 1 \times 1 = 1,\ 1 \times 2 = 2,\ 2 \times 3 = 6 \\ &6 \times 4 = 24,\ 24 \times 5 = 120,\ 120 \times 6 = 720 \end{aligned} \]
That is \(0!, 1!, 2!, 3!, 4!, 5!, 6!\), and \(5! = 120\). The last term confirms it, since \(120 \times 6 = 720\). 100 and 140 do not lead to 720 by any consistent rule (720 is not a whole multiple of 140), and 13 breaks the steady growth of the series.
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