Can a sequence be called convergent/divergent if it has finite number of terms?

No explanation required for the question I guess.

1 Answer

Yes. A finite sequence is convergent.

Call your sequence $\{a_k\}$. It is finite, so it has a last term, say $a_m=M$.

An sequence converges to a limit $L$ if for any $\epsilon>0$, there exists some integer $N$ such that if $k\ge N$, $|a_k-L|<\epsilon$. However, since your sequence is finite, for any $\epsilon>0$ we just take $N=m$, and it is clearly true that if $k\ge m$, $|a_k-L|=|a_m-L|=0<\epsilon$, since the only possible value for $k$ is $M$ itself.

I hope that was not too confusing.