Write your synopsis as you would were this a stand-alone book instead of one installment in a multi-volume storyline—except that in the final paragraph, when you state how this volume’s problem was resolved, you add a line or two pointing out that the overarching series problem still festers. Then offer an additional paragraph, set off from the main synopsis by a line space, that presents your 40ish-word hook for the next volume. You’ll have already pitched your full trilogy or series in your query letter; adding the hook here gives context for the thread you’ve left dangling in this synopsis. If your character gained a particular strength or fact in this volume that is integral to the plot of the next one, point that out in the hook to emphasize the link between the volumes.
I’ve only written books capable of standing alone, but I really appreciate the advice on how to write a synopsis for a series in case I ever write one. Thanks! 🙂