What you're looking for is lists.
You would do that bit of C# code like this in TIBasic:
However, keep in mind several differences between TIBasic and more sophisticated languages like C#. First, you can't declare integer lists. There is only one kind of list: floating point. So a 1000-element list would take up an obscene amount of memory on a calculator. Also, the list index starts at 1, not 0. There is also no undefined or null element: only numbers can go in lists. Also, the size of a list can change; so there's no need to initialize the list with 1000 elements (unless you were doing something like a Sieve of Erasasdfjkl). You can simply store the next value to the next unused list index: 3→∟PRMS(2
Anyway, welcome to this site! If you'd like to learn more about TI-Basic, just ask! And of course, you can always look through the wiki, which has many useful resources for beginners. :D