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 $-\dfrac{1}{2}$, $\dfrac{1}{4}$, $-\dfrac{1}{8}$, $\dfrac{1}{16}$, $-\dfrac{1}{32}$.