I would like clarification on the following definition of finite arithmetic progression:
According to Wikipedia, "A finite portion of an arithmetic progression is called a finite arithmetic progression and sometimes just called an arithmetic progression. The sum of a finite arithmetic progression is called an arithmetic series." https://en.wikipedia.org/wiki/Arithmetic_progression
Is there a minimum as to how many terms ($a+nd$) must belong to a progression before it's "finite"? It would be at least two, right? For example: $a+nd$, $a+$($n+1$)$d$ = 3, 23 (where $a$ = 3, $d$ = 20, $n \geq 0$).
Mathematics tends to prefer general definitions.
For example, a function $f: \mathbb{Z} \rightarrow X$ mapping from the integers is typically considered continuous (under the discrete topology). You might argue that such a function doesn't "feel" continuous, or that it's not "useful" to extend the definition in this way, but in reality, it's more work to gatekeep trivial objects from satisfying the definition at hand. You should only exclude edge cases if they simplify the theory you are working towards.
All of this is to say that there might be nothing wrong with allowing a single term sequence to constitute a finite sequence. If nothing else, it saves you from having to stipulate at what point something is special enough to "become" a finite sequence (is it 2 terms? 3 terms?).
As I post this, I see that @jjagmath has answered with a comment making a similar observation; apologies for the overlap