A sequence of real numbers is a function whose domain is an infinite set of natural or integer numbers, and its "path" is a subset of real numbers. The notation $x_t$ is used to describe the values of the sequences, $f (t) = x_t$. $$f (t) = x_t: A\subseteq \mathbb{N} \Rightarrow \mathbb{R}$$
The OA sequence:
If the distance between two consecutive terms decreases, the sequence is called OA, it is to say: $$|x_{t+2}-x_{t+1}|<|x_{t+1}-x_{t}| $$ For any t.
Limit of a sequence:
We know that a sequence $x_t$ converge to $L$, if and only if: $$\lim_{t\to \infty} x_t=L$$
My question is: Does it exist a OA sequence that diverges?