The second line of the Format menu when the TI-83 Plus graphing calculator is in Sequence mode gives you a choice: You can display the coordinates of a point in rectangular form (RectGC) or polar form (PolarGC). The first line offers various formats for graphing sequences. Assuming you’ve selected RectGC, here is what the calculator graphs in each format on the first line of the menu:

• Time: This is the most common format for graphing sequences because it graphs the sequences as a function of the independent variable n. That is, in the Time format, the points (n, u(n)), (n, v(n)), and (n, w(n)) are graphed.

• Web: This format produces a web plot (also known as a cobweb plot because of its shape) for a sequence u(n). Use it when you want to see whether u(n) converges to an equilibrium point or just veers off into space. It graphs the points (u(n), u(n + 1)) and the line y = x. Using the [TRACE] and

keys then shows you whether the sequence is converging or diverging.

In web format, the calculator places two restrictions on how the sequence u(n) is defined. First, it requires that u(n – 1) appear as a variable in the definition of u(n); second, it requires that u(n – 1) be the only variable used in this definition.

Defining u(n) as u(n) = u(n – 1) + u(n – 2) or as u(n) = v(n – 1) results in an error message. And because u(n) = u(n – 1) + n uses the variable n in its definition, it too results in an error message when it’s used in the web format.

• uv, vw, and uw: Use these formats to create phase plots when you want to see how one sequence affects another sequence. The uv format graphs the points (u(n), v(n)); the vw format graphs the points (v(n), w(n)); uw format graphs the points (u(n), w(n)).

When you’re graphing sequences, there’s no harm in leaving these items highlighted.