Consider the positive integer sequence
\[x_{n}=n^{50} e^{-(\log (n))^{3 / 2}}, \quad n=1,2,3, \ldots\]
Which of the following statements is $\text{TRUE?}$
- For every $M>0$, there exists an $n$ such that $x_{n}>M$
- Sequence $\left\{x_{n}\right\}$ first increases and then decreases to 1 as $n \rightarrow \infty$
- Sequence $\left\{x_{n}\right\}$ first decreases and then increases with $n \geq 1$
- Sequence $\left\{x_{n}\right\}$ eventually converges to zero as $n \rightarrow \infty$
- None of the above