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Question

# List the first five terms of the sequence. \$\{2 \cdot 4 \cdot 6 \cdots \cdots \cdot(2 n)\}$

Solution

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In order to find each of the terms, all we need to do is plug the different values for $n$ into the expression (from 1 to 5):

\begin{align*} a_1 &= (2 \cdot 1) = 2 \\ a_2 &= 2 \cdot (2 \cdot 2) = 2 \cdot 4 = 8 \\ a_3 &= 2 \cdot 4 \cdot (2 \cdot 3) = 2 \cdot 4 \cdot 6 = 48 \\ a_4 &= 2 \cdot 4 \cdot 6 \cdot (2 \cdot 4) = 2 \cdot 4 \cdot 6 \cdot 8 = 384 \\ a_5 &= 2 \cdot 4 \cdot 6 \cdot 8 \cdot (2 \cdot 5) = 2 \cdot 4 \cdot 6 \cdot 8 \cdot 10 = 3840 \end{align*}

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