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The readers must not be surprised by it. The marketing for the second book must make it clear what is going on. If you just say "The long-awaited sequel to Book 1", people will buy Book 2, but fe...
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#3: Attribution notice added
Source: https://writers.stackexchange.com/a/26037 License name: CC BY-SA 3.0 License URL: https://creativecommons.org/licenses/by-sa/3.0/
#2: Initial revision
The readers must not be surprised by it. The marketing for the second book must make it clear what is going on. If you just say "The long-awaited sequel to Book 1", people will buy Book 2, but feel cheated and will never buy Books 3 and 4. (And your other books outside this series) If you say "The adventures for Y, set in the same world as Book 1", people will know what is going on. Somewhat fewer people will buy Book 2, but they will not feel cheated and will probably continue to buy Books 3 and 4. Of course, people will want to know what happened to the original protagonist after the end of Book 1. You should cover some of that between the action of the new book. It helps a lot if the new protagonist has a significant role in the first book, to make readers care about their story. That way you can drop the "Set in the same world" part since everybody understands that. You gave an example of a family saga, where the new protagonist is just a baby in the first book. In that particular case, you can prime the readers to be interested in the next book by having the parents think about "How is the world going to be when Junior grows up?" Having them worry about this, you also make the readers worry about it... and then there is a new book just about that, how nice!