Discussion

Find the missing term in the series

2, 5, 14, 41, ______

Answer: A

The missing term is 122.

Each term is three times the previous one, minus 1.

\[ \begin{aligned} 2 \times 3 - 1 &= 5 \\ 5 \times 3 - 1 &= 14 \\ 14 \times 3 - 1 &= 41 \\ 41 \times 3 - 1 &= 122 \end{aligned} \]

The differences 3, 9, 27 confirm it: the next difference is 81, and \(41 + 81 = 122\). 124 would be \(41 \times 3 + 1\), the wrong sign.

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