Part of looking at the big picture means not only making plans for further installments, but making sure that those further installments also involve good plotting and storytelling.* The series has to work, as well as the individual books.
Because, let's face it, we use the term 'series' to describe two very different things. One type, like Lord of the Rings of The Belgariad, is actually a single story, which happens to be broken down into several separate books, for one reason or another.** The other type, like Harry Potter, tells an overarching story, but each books stands on its own as an individual unit. The latter is the type I prefer, and that's what I intend to write. But the overarching story needs to pay off, as well as the individual books.
This is where I go back to the Twelve-Part Structure. It can apply to whatever grand arc-plot the series has, as well as each individual book. How much of the twelve-part structure goes into each book, that depends on how many books you plan for your series.*** Trilogies are easy to break down. Tetrologies work, but come out a bit odd in the twelve-part structure. Pent- and Heptologies, which seem to be the very popular****, don't necessarily break cleanly, but that isn't a big deal. But personally, I like the Hexology. Possibly because it breaks down so cleanly with my twelve-part structure. So this is how it works for the Hexology, though it's pretty easy to re-work it as you see fit for however many books you think your series should have.
Book 1: Establishment and Incitement. This is pretty clear, as any first book in a series need to set establish the players of the larger arc-plot, and lay the hints for the bigger things to come. On the whole, this story needs to stand on its own the most, for obvious reasons.
Book 2: Challenge and Altercation. The plot of this story needs to turn the screws tighter on the larger plot. Here, really, is where your main characters realize that something bigger is looming, and they will have to deal with it. More important is, though, is that in Book 2 your main characters need to be challenged far beyond whatever Book 1 did to them, they need to push themselves further than they thought they were capable of, and they should prevail.
Book 3: Payback and Regrouping. On some level, Book 3 should be a dark mirror of Book 1. In the grand scheme of things, Book 1 is a romp (even if it leaves plenty of bodies on the floor). Book 3 should make the problems of Book 1 look like fun and games. But even with that, it can feel like conclusion, in terms of the arc. It can feel like, despite the things your heroes go through, everything is going to be all right.
Book 4: Collapse and Retreat. Everything isn't going to be all right. This is where the hammer drops. On whatever sliding scale you use, Books One through Three were walks in the park. Book 4 doesn't leave scars, it leaves walking wounded. This phase of your arc needs to be about despair. Even if the individual plot of Book Four can be considered a "victory" for your heroes, it's a Pyrrhic one at best. Things will not be the same after this.
Book 5: Recovery and Investment. The arc is in a dark place in the beginning of Book 5. The dark place is the "new normal" that the characters need to believe they live in, and the plot of Book 5 needs to be their fight back to the light. This is where they consider quitting. This is where they decide they can't do that.
Book 6: Confrontation and Resolution. The last book is, of course, about wrapping up the arc plot.
That's how I break it into six books, but like I said, it's easy to shift and shuffle that for however many books your series is. Take, for example, a classic example of seven: Harry Potter.
Sorcerer's Stone (Establishment and Incitement): Harry learns about the magical world and his history (Establishment) and makes the decision that he stands against Voldemort and what he represents (Incitement).
Chamber of Secrets (Challenge and Altercation): Harry learns that the legacy of Voldemort has deeper roots than he expected, and it's still effecting his life (Challenge), and in facing Tom Riddle and the basilisk, he steps up to actively fight that legacy (Altercation).
Prisoner of Azkhaban (Payback and Regrouping): Harry faces uncomfortable truths about his parents, having to confront his own fears directly (Payback). He stands up to those fears, masters the Patronus, is able to fight off the Dementors, and gains some apparent stability through his relationship with Sirius (Regrouping).
Goblet of Fire (Collapse): Voldemort is back and Cedric is dead. Things just got serious.
Order of the Phoenix (Retreat and Recovery): Harry is devastated, ridiculed and tormented over the events of Goblet, and through Umbridge, the system itself is against him (Retreat). Despite that, he pulls it together and creates Dumbledore's Army, and refuses to go along with the lies of the Ministry (Recovery).
Half-Blood Prince (Investment): In learning the full scope of what it will take to stop Voldemort, and losing Dumbledore, Harry decides it is his responsibility to defeat Voldemort.
Deathly Hallows (Confrontation and Resolution): Harry goes after the horcruxes (Confrontation), and then faces Voldemort in the Battle of Hogwarts. (Resolution).
See? The structure of the arc is there, yet each of those seven books also have their own story structure. I haven't gone through to figure out if each of the seven books individually match the twelve-part structure, but I bet they come close.
*- This is, of course, getting ahead of myself, but I always like to keep looking at the map while I'm on the road.
**- I've heard that, in the case of LotR, it had to do with binding machines at the time wouldn't be able to handle the full text. For the Belgariad, it was pure business- Lester del Ray could make more money selling five books instead of three, as Eddings had originally planned.
***- I will not go on a rant about series that have indeterminate lengths.
****- Why is that? Is it the prime numbers?