Define a recursive sequence and its relationship to a fibonacci sequence

The Fibonacci sequence is a series of numbers where a number is found by adding up the two numbers before it. Starting with 0 and 1, the sequence goes 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, and so forth. Written as a rule, the expression is xn = xn-1 + xn-2.
A recursive sequence , also known as a recurrencesequence, is a sequence of numbers indexed by an integer and generated by solving a recurrence equation. The terms of a recursive sequences can be denoted symbolically in a number of different notations, such as , , or f[ ], where is a symbol representing the sequence.