Writing the Terms of a Sequence

Write the first five terms of the sequence \[ \{a_{n}\} =\left\{ (-1)^{n}\left( \dfrac{1}{2}\right) ^{n}\right\} \]

Solution The \(n\)th term of this sequence is \(a_{n}=(-1)^{n}\left(\dfrac{1}{2}\right) ^{n}\). So, \[ \begin{eqnarray*} a_{1}&=&(-1)^{1}\left(\dfrac{1}{2}\right) ^{1}=-\dfrac{1}{2}\quad a_{2}=(-1)^{2}\left(\dfrac{1}{2}\right) ^{2}=\dfrac{1}{4}\quad a_{3}=(-1)^{3}\left(\dfrac{1}{2}\right) ^{3}=-\dfrac{1}{8}\\[6pt] a_{4}&=&\dfrac{1}{16}\quad a_{5}=-\dfrac{1}{32} \end{eqnarray*} \]

The first five terms of the sequence \(\{a_{n}\}\) are \(-\dfrac{1}{2}\), \(\dfrac{1}{4}\), \(-\dfrac{1}{8}\), \(\dfrac{1}{16}\), \(-\dfrac{1}{32}\).