Upper bound of a set and a sequence

Question

If the excercise says:

Let $a \in \mathbb{R}$ be an accumulation value of the real sequence $(a_{n})_{n\in\mathbb{N}}$ and an upper bound of the set $\{a_{n}\ |\ n\in\mathbb{N} \}$.

Does is mean that $a$ is also the upper bound of the real sequence $(a_{n})_{n\in\mathbb{N}}$?

Answer 1

Every convergent sequence is a bounded sequence, that is the set {$a_n : n ∈ \mathbb{N}$} is bounded.