For a sequence a1 a2 a3 a n explicit formula is a formula that can compute the value of a n using its location. For example the Fibonacci sequence which starts 0 1 1 2 3 5 8 with each successive term being the sum of the previous two. Each term is found by doing something to the terms immediately in front of that term A recursive formula designates the starting term a 1 and the n th term of the sequence a n as an expression containing the previous term the term before it a n-1.
While this apparently defines an infinite number of instances function values it is often done in such a way that no infinite loop or infinite chain of references.
For a sequence a1 a2 a3 a n explicit formula is a formula that can compute the value of a n using its location. A n a n-1 15. A recursive formula is a formula that requires the computation of all previous terms in order to find the value of a n. For example the Fibonacci sequence which starts 0 1 1 2 3 5 8 with each successive term being the sum of the previous two.