To find the statement that describes the sequence, we find it's limit as n goes to infinity.
Doing this, as we get that the limit goes to infinity, we get that the sequence diverges.
Sequence:
[tex]a_n = \frac{n^3 + 3n}{n^2 - 6n}[/tex]
Limit as n goes to infinity:
Limit of n going to infinity, so we consider just the terms with the highest exponent in the numerator and in the denominator.
[tex]\lim_{n \rightarrow \infty} a_n = \lim_{n \rightarrow \infty} \frac{n^3 + 3n}{n^2 - 6n} = \lim_{n \rightarrow \infty} \frac{n^3}{3n^2} = \lim_{n \rightarrow \infty} \frac{n}{3} = \frac{\infty}{3} = \infty[/tex]
Thus, the correct answer is that the sequence diverges.
For more on limits going to infinity, you can check https://brainly.com/question/23335924
