# How to Graph a Recursive Sequence on the TI-84 Plus

You can use the TI-84 Plus calculator to graph a recursive sequence and to graph the much more difficult Fibonacci sequence, one of the most famous sequences in mathematics.

## Graphing a recursive sequence

In order to contrast explicit and recursive sequences, in this example, use the same arithmetic sequence: 2, 5, 8, . . .

Recursive formula for an arithmetic sequence: *a*_{n} = *a*_{n–1}+d

The recursive formula for this sequence is *a*_{n}** = ***a*_{n–1}**+3**, where *a*_{1}=2. In this formula, *a*_{n–1} represents the previous term. In Sequence mode on the calculator, the previous term is *u*(*n*–1). Follow these steps to enter a recursive sequence in your calculator:

Press [Y=] to access the Y= editor.

Enter a value for

*n*Min.*n*Min is the value where*n*starts counting.Press [TRACE] to enter the variables,

*u*,*v*, and*w*, as shown in the first screen.Enter the recursive formula for

*u*(*n*).Don’t forget to press

for

*n.*Enter

*u*(*n*Min).Enter the initial term as shown in the second screen.

Press [GRAPH.

The graph of this sequence looks exactly like the graph of the explicit function as shown in the third screen.

## Graphing the Fibonacci sequence

Want to try something more difficult? The Fibonacci sequence is one of the most famous sequences in mathematics: 1, 1, 2, 3, 5, 8, . . .

The recursive formula for the Fibonacci sequence is: *a*_{n} = *a*_{n–1}+* a*_{n–2}. Remember, *u*(*n*–2) means the term before the previous term in calculator lingo.

Press [Y=] to access the Y= editor.

Enter a value for

*n*Min.*n*Min is the value where*n*starts counting.Press [2nd][TRACE] to enter the variables

*u*,*v*, and*w.*Enter the recursive formula for

*u*(*n*).Enter

*u*(*n*Min).Enter the first two terms in the sequence as a list! Press [2nd][(] to use brackets for your list. See the first screen.

Press [WINDOW] and adjust the variables.

The value of Ymax was changed. See the second screen.

Press [GRAPH].

See the third screen.

Did you notice all the tick marks on the

*y*-axis in the third screen? It would have been a good idea to change the Yscl to 5 or 10. Press [WINDOW] to access the Yscl variable.