Answer
Eventually strictly decreasing.
Work Step by Step
Consider $$f(x)=\left\{\dfrac{x}{x^2+10}\right\}$$ Then
\begin{align*}
f'(x) &=\dfrac{10-x^2}{(x^2+10)^2}\\
&=(1-2x)e^{-2x}\lt 0
\end{align*}
We see that $f'(x) \lt 0$ for $x \geq 4$. This implies that the given sequence is eventually strictly decreasing.
