Answer
Converges to $1$.
Work Step by Step
$\lim\limits_{n \to \infty}a_{n}=\lim\limits_{n \to \infty}tan(\frac{2n \pi}{1+8n})$
$=tan \lim\limits_{n \to \infty}(\frac{2n \pi}{1+8n})$
$=tan \lim\limits_{n \to \infty}( \frac{\pi}{4})$
$= \lim\limits_{n \to \infty}tan ( \frac{\pi}{4})$
$=1$
The given sequence converges to $1$.
