After you’ve graphed your sequences on the TI-83 Plus graphing calculator, you can save the graph and its entire Window, Y= editor, Mode, and Format settings in a Graph Database. When you recall the Database at a later time, you get more than just a picture of the graph.

The calculator also restores the Window, Y= editor, Mode, and Format settings to those stored in the Database. Thus, you can, for example, trace the recalled graph.

After you’ve graphed your sequences, you can draw lines and functions on the graph, write text on it, and save a picture of the graph and the drawings. This capability is handy if you want to illustrate the way a sequence converges to a number, or show that a sequence can be approximated by a function.

A sequence is simply an ordered list of terms or numbers. The most famous sequence is perhaps the Fibonacci sequence, {0, 1, 1, 2, 3, 5, 8, 13, . . .}, where the first two terms are given and the remaining terms are found by adding the previous two terms.

The formula used to generate a sequence is referred to by various names, such as a recurrence relation, a recursive function, or an iterative function. Texas Instruments calls these formulas sequence functions.

In spite of the power of the calculator, it’s rather limited when dealing with sequence functions. It can accommodate only three sequence functions, and each function can address only the previous two terms of that function (or of another function). So the calculator can handle the Fibonacci sequence, u(n) = u(n – 1) + u(n – 2), but nothing fancier.