Answer
Diverges
Work Step by Step
It is given a sequence $a_n=5\sqrt{n+1}$.
Substituting $n=1,10,20,30,\ldots,80$, we get the graph of the sequence as in the figure.
We can see that the value of $a_n$ increases without bound as $n$ becomes larger.
It indicates that the limit of $a_n$ is infinity.
We write $\lim\limits_{n \to \infty}a_n=\infty$.
So, the sequence diverges.
