How is the recursive form of a sequence sometimes more useful than the closed form (where a rule is found to find any term based on its position in the sequence)?

The recursive form is very useful when there aren't too many terms in the sequence. For instance, it would be fairly easy to find the 5th term of a sequence recursively, but the closed form might be better for the 100th term. On the other hand, finding the closed form can be very difficult, depending on the sequence. With computers or graphing calculators, the 100th term can be found quickly recursively

What’s the improper fraction?