Answer
$\lim\limits_{n \to \infty} a_n=0$ and {$a_n$} is convergent.
Work Step by Step
Let $\lim\limits_{n \to \infty} a_n= \lim\limits_{n \to \infty}
(\dfrac{-1}{2})^n$
Since, we know that $|\dfrac{-1}{2}|=\dfrac{-1}{2} \lt 1$.This means that $ \lim\limits_{n \to \infty} (\dfrac{-1}{2})^n=0$
Hence, $\lim\limits_{n \to \infty} a_n=0$ and {$a_n$} is convergent.
