There are two kinds of series: (a) What is really one very long story that is broken into pieces for convenience or marketing purposes. That is, if a story takes 1000 pages, rather than try to sell one 1000-page book, we instead make a trilogy and sell three 330-page books. This makes each book more manageable and makes pricing more realistic. Etc. (b) A story that is a series in the sense of distinct episodes that have common characters and/or a common setting, but that are distinct, stand-alone stories.
For a story to work well as a series, each installment has to pretty much end up where it started. That is, a problem was presented, the characters solved it, and now things are returned to "normal", ready to attack the next problem.
Consider the detective story. This works very naturally as a series. In each installment, a crime is committed and the brilliant detective solves it. Once he's solved it, it's done, and he's ready to take on the next case.
Or consider the typical TV family comedy. Members of a family have some problem, they solve it, and now order in the family is restored. They are ready to face the next problem. (Usually the solution turns out that it was all a misunderstanding, because if somebody was truly in the wrong, then one of the main characters is now less likeable, which is a problem for the series.)
Some stories do not work well as a series, because once the problem is solved, it would be very unlikely for a similar problem to come up. Like take the classic romance story: the heroine meets the hero, they fall in love, they overcome some obstacles to their love, and then they live happily ever after. So once you end with the happy couple getting married (or these days, simply moving in together), where do you go from there? If the next installment the heroine is chasing after some other man, than apparently they didn't live happily ever after after all. To start a new romance we have to say that in fact the first romance was a failure and not the success that it was painted. So okay, you might, you might say that the first husband turned out to be a jerk and now the heroine is divorced and in pursuit of romance again. But there's a limit to how far we can go with this. We might buy that she was unlucky in love two or three times. But after the 15th failed marriage, we're going to think there is something wrong with this woman.
You could, of course, go off in a different direction. You could say that now that they're married, we explore their married life, or they start solving crimes together, or whatever. But in that case it's not a "romance series", it's a "detective series" where the first episode was a prologue that explains how the two detectives got together. I suppose in principle you could have a series with the same characters and they do totally different things in each installment. In book 1 they have a romance and get married. In book 2 they solve a crime together. In book 3 they become doctors and treat a difficult patient. Etc. But who would want to read such a series? Each book would appeal to fans of a different genre. And after a while it would get ridiculous: Are these people experts at EVERYTHING?
In my humble opinion, a major element in making television so uncreative is that it is largely limited to the series format. Only so many ideas work as a series: the detective solves a series of crimes, the lawyer handles a series of cases, the doctor treats a series of patients, the family deals with a series of misunderstandings, the spaceship visits a series of planets. Those five ideas probably make up about 90% of TV series, because they're ideas that work as series.
Earlier I said that in a series, each installment has to end where it began. It doesn't have to end EXACTLY where it began. The problem can be solved and the characters ready to deal with another problem, but their relationships might change and develop, the characters might learn new things, etc. But then that requires that the installments be read/viewed in order. In TV, for example, episodes are often re-run during the summer, sold to syndication, etc, so the producers don't know what order people will see episodes in. So TV series often make sure they really do end each episode EXACTLY where it started.