Here is the recursive definition of a sequence: for .

1. List the first 5 terms of the sequence.

2. Graph the value of each term as a function of the term number.

Here is a graph of sequence . Use function notation to define recursively.

Graph of a sequence Q. Horizontal axis, "n," with scale from 0 to 6, by 1’s. Vertical axis, with scale negative 5 to 10 by 1’s. Coordinates plotted (1 comma negative 3), (2 comma 0), (3 comma 3), (4 comma 6) and (5 comma 9).

Here is a recursive definition for a sequence :  for . The definition for the term is   for .

1. Explain how you know that these definitions represent the same sequence.
2. Select a definition to calculate , and explain why you chose it.

An arithmetic sequence starts 20, 16, . . . Explain how you would calculate the value of the 500th term.