First, FrankW is right about you having to provide what he calls a set of examples (way of constructing a tree with those properties for most $n$ / a generic recipe)
However, while this set doesn't have to contain an example for every value on $n$, it should contain an example for every value above a certain $n_0$, which would also be a part of your solution (check the definition of $\Theta$, google "Big Oh"). In other words, for each $n$ above a certain $n_0$ (that you need to figure out), you need to able able to construct a tree with your desired properties for that $n$.
I also think you would have to clarify what exactly you mean by Width being $\Theta(n)$. Does that mean the Width of every level is in class $\Theta(n)$, or that the final (bottom) level is? Does it matter?
As for constructing the tree, here's a couple of guides that are hopefully not mistaken and leave a bit work for you to do yourself
- What's the minimal tree of height $n$ that you can come up with? What is its width at the bottom level?
- Is there a way of increasing the width of the minimal tree of height $n$ by one while keeping its height?
- Can you apply 2. until you get to width $n$?