Write the first four terms in the list of numbers defined by $a_{n} = {(- 1)}^{n - 1} n^{4}$

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Solution

Write the first four terms of sequence $a_{n} = {(- 1)}^{n - 1} n^{4}$ by substituting $n = 1, 2, 3, 4$ :
$\begin{array}{rcl} \Rightarrow & a_{1} = {(- 1)}^{1 - 1} 1^{4} \\ = & 1 \\ \Rightarrow & a_{2} = {(- 1)}^{2 - 1} 2^{4} \\ = & - 16 \\ \Rightarrow & a_{3} = {(- 1)}^{3 - 1} 3^{4} \\ = & 81 \\ \Rightarrow & a_{4} = {(- 1)}^{4 - 1} 4^{4} \\ = & - 256 \end{array}$
Therefore, the first four terms of sequence is $1, - 16, 81, - 256$ .

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