Discussion
Find the next number to the following .... 1, 1, 2, 4, 8, 12, 144, 1728, ......
Answer: B
The next number is 1872.
After the opening 1, 1 the series repeats a cycle of three operations: add the last two terms, square the result, then multiply the last two terms.
\[ \begin{aligned} 1 + 1 &= 2, \quad 2^{2} = 4, \quad 2 \times 4 = 8 \\ 4 + 8 &= 12, \quad 12^{2} = 144 \\ 12 \times 144 &= 1728 \end{aligned} \]
The next step in the cycle is addition again: \(144 + 1728 = 1872\).
The other options do not come from any of the three operations applied to 144 and 1728: their product and the square of 1728 are far larger, and no step of the cycle subtracts.
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