Got an email the other day from one of my fellow authors who does editing on the side. She's in the middle of editing a novel for another author, in this case a second book within a series. She never read the first book, and the author is apparently making a mistake novice fiction writers sometimes make--that is assuming readers will have already read the first book. As a result, she found some passages to be very confusing, to say the least, making it difficult for her to do her job.
I recall making that mistake once myself. I'd just published Gunfight at the O.K. Corral, the first book in my Luke and Jenny series. As I began working on the manuscript for the second book, Billy the Kid and the Lincoln County War, I too went on the assumption that readers would have already read the first book, so I was writing accordingly. Lucky for me, my publisher clued me in. I seem to recall sending her an early draft of the first few chapters, and she caught the error before I'd gone too far. She told me to never, ever assume that the reader has read the first book. Even if they had, it wouldn't be beyond the realm of possibility for a considerable amount of time to have passed before starting the next book. She told me to go on the assumption that the reader had not read the prior book, and write accordingly.
When writing a series you don't need to include a complete summary of the previous book(s). What
you will need to do is write a few brief sentences, perhaps a paragraph, when appropriate, with just enough relevant information so your reader can understand, or recall, the back story and how it relates to the current plot. You can do this in the narrative. It's even better if you can work it into the dialog.
Don't leave your readers in the dark and never assume that they've read your earlier book(s). Bring them up to speed, as quickly as possible, so they can understand your story and follow the plot. Otherwise you'll end up with a frustrated, confused reader, who may very well toss your book aside without ever finishing it.
My tip for the day.