Trilogies
In answer to the two questions raised: I had only completed the first book; and yes, it was my first book deal.
My particular trilogy was not much worked out at all beyond Book 1. I did not even supply a synopsis of Books 2 and 3. I just let it be known through my agent that I envisaged follow-ups, and I think I gave them titles, which never hurts. The possibility of "more to come" was apparent in that the end of Book 1 hinted (as film endings sometimes do) that not everything was done and dusted. However, the novel was a complete entity, in that - to put it crudely - the good guys came through and disaster was averted (this time, kind of thing.) In that sense it was not a trilogy like The Lord of the Rings, where the big issues are obviously not resolved at all in Books 1 or 2. I would imagine that my kind (i.e. complete stories with a suggestion of more to come) are an easier sell than the LOTR kind. Another key factor, of course, is establishing characters that readers are happy to meet again (at least some of them). I think this was what swung it with my first publisher.
As a PS: in the event, when the first book did not do all that well, and my editor left, and I saw how my titles were becoming very low priority at my publishers (the pissy Book 2 catalogue position was a giveaway), I actually ditched the 3rd part of the trilogy and wrote it as a stand-alone with new characters and an altered story (the publisher, of course, did not mind a bit). This was my salvation, becase I sold that book internationally - most importantly in the US, where it did very well and rescued what would otherwise have been a rather brief career. This would never have happened if I had loyally plodded on and completed the trilogy.
Such radical measures are needed when trilogies go wrong!