OK, feel free to call it “sequence” instead of “series”.
So, in some cases infinite sequence of something is possible, and in some cases it is not possible.
Very good. Looks like we agree here.
Then, have you thought what happens in the specific case relevant for the First Way?
And that is completely irrelevant for that example.
Perhaps it would be better to talk not about “events” (that might create an impression that we are dealing with “accidentally ordered series of causes”), but about just “causes” or, perhaps, “objects”…
Mathematics is irrelevant to the context of what is being described. If a series of beings moving from potential to actual is infinite, and If every effect in the series is only potentially actual, then every cause in the series is also only an effect. Therefore every cause and effect in the series is only mediating actuality because existence does not originate in either cause or effect. No effect in the series is the cause of it’s existence. Therefore the reason why there is an infinite series of actual movers cannot be found in the series itself because the series, regardless of the fact that it is infinite, is not what causes actuality or existence. The whole series is an effect that is being given existence as opposed to being the cause of it. Since the series itself cannot be the cause of it’s actuality because every cause in the series is also an effect, it’s existence must be caused by that which is pure-actuality or that which is it’s own existence; otherwise the series cannot exist.