When you write the first book in a series, you can do anything you want.
When you write the second, you can still do anything you want… but whatever you do that repeats or echoes the first book, becomes part of the shtick of that series, and your audience will expect you to do it again.
Think about Harry Potter. You read the first book, in which there is a prologue, then Harry has a sequence in Muggle England, then he goes off to Hogwarts for a year of school.
At that point — the end of book one — the series could have looked like anything. In the next book, Harry could have become an astronaut. But parts of book two echo book one (Harry has a persecuted sequence in Little Whinging, travels to Hogwarts and goes through one year of school), so those parts become the shtick of the Harry Potter, and we expect to see them repeated in subsequent books (and we do). Some parts of book one are not echoed in book two: book two has no prologue, for instance, and thereafter prologues are not a necessary part of the series (some books have them, and some don’t).
E.J. Patten of the Story Monkeys wrestled with this recently in crafting the sequel to his epic horror middle reader book Return to Exile (released TOMORROW). He had to consciously choose which parts of book one to repeat or echo, knowing that then he would be using them (or riffing on them) again in books three and so on.
And I recently read Endymion, book three of Dan Simmons’s Hyperion Cantos. And this book… man, it just didn’t live up to books one and two. Part of that may just be ordinary series fatigue (see Star Wars, Indiana Jones, Dune, etc.), but also, I think my expectations as the audience were violated.
See, the first two books — Hyperion and The Fall of Hyperion — were really doggone smart. Hyperion was actually very self-consciously literary, modeling itself on the Canterbury Tales, but the sequel dropped that conceit, so I knew literary models were not part of the series shtick (it would have been cool if book two was a science fiction take on Beowulf, but oh, well). But the first two books were both cleverly plotted, with surprising ends.
And book three was not. It violated my series expectations. It was fine, it wasn’t bad. It continued the plot of the first two, more or less, and if it had been the first book of a series I probably would have enjoyed it without any complaint. But its change of heart twist at the end was nothing like the surprises of the first two books (and was fairly predictable). Add some mostly two-dimensional characters, and my goodwill for the series and author and the book’s own actual high concept coolness (it’s sort of Riverworld meets Terminator 2) weren’t enough for me. My expectations are violated, I don’t know if I’ll be able to pick up book four. Certainly, not for a while.