Does convergence by the ratio test for sequences implies that the sequence is monotonic?

Question

I wonder, Let's say $(a_n)_n$ is a sequence.

If $ \frac{a_{n+1}}{a_n} \to L $ and $ L<1$. Then $ a_n \to 0 $.

But, does it mean that $a_n$ is monotonically decreasing? (For every $n$, $a_n > a_{n+1} $ ) ?

Thank you.