Question

You are given the first four terms of an arithmetic sequence. Under what
conditions might a recursive formula be preferred over the explicit formula?
Under what conditions might an explicit formula be preferred over the
recursive formula?

Answer 1

If you need to know the 7th, 8th, and 9th terms, the recursive form might be preferred as you need to apply the common difference successively to the next few terms. If you want to know terms, such as those beyond 100,
then the explicit would be preferred