After you have graphed your sequences on the TI-83 Plus graphing calculator, press [TRACE] and then use the right arrow key to investigate the sequence or sequences. Here’s what you will see, and what you can do to change things:

• The definition of the sequence: The definition of the sequence you’re tracing is displayed in the upper-left corner of the screen, provided the calculator is in ExprOn format. If you have graphed more than one sequence and you would like to trace a different sequence, press

Each time you press this key, the cursor jumps to another sequence. Eventually it jumps back to the original sequence.

• The independent variable n: The value of n corresponding to the cursor location is displayed in the lower-left corner of the screen, provided the calculator is in CoordOn format. When you press [TRACE], the cursor is placed at the beginning of the graph of the sequence and n displays the value you assigned to nMin in the Window editor. Each time you press

the cursor moves to the next plotted point in the graph — and the value of n changes to the value of the independent variable corresponding to that plotted point.

If you press

the cursor will move left to the previously plotted point in the sequence. And if you press

to trace a different sequence, the tracing of that sequence will start at the same value of n that was displayed on-screen before you pressed this key.

When you’re using TRACE, if you want to start tracing your sequence at a specific value of the independent variable n, just key in that value and press [ENTER]. (The value you assign to n cannot be greater than nMax; if it is, you will get an error message.) After you press [ENTER], the trace cursor moves to the point on the graph corresponding to that value of n.

But the calculator does not change the viewing window. So if the value you assigned to n is greater than Xmax, you won’t see the cursor; it’s on the part of the graph outside the viewing window.

• The values of x and y: At the bottom of the screen you see the values of the x- and y- coordinates of the cursor location, provided the calculator is in CoordOn format. In the PolarGC format, the coordinates of this point display in polar form. The relationship between these coordinates and the sequence depends on how you set the format for the sequence.

Here’s what you will see in the various formats:

• Time format: In this format the x-coordinate is the independent variable n and the y-coordinate is the corresponding value of the sequence at n.

• In the web format: In this format, the trace cursor starts on the x-axis at the first term in the sequence u(n). When you press

the cursor moves vertically to the graph of the points (u(n), u(n + 1)). And when you press

again, it moves horizontally to the line y = x. Each time you press

after that, the cursor repeats this alternating vertical and horizontal movement. In addition, a vertical or horizontal line connects all points traced by the cursor.

In web format, if nMin =1, the points traced by the trace cursor are (u(1), 0), (u(1), u(2)), (u(2), u(2)), (u(2), u(3)), (u(3), u(3)), (u(3), u(4)), and so on. You use this format when you want to see if a sequence converges or diverges. Here is an example of using the web format and TRACE to investigate the convergence of a sequence.

• uv, vw, and uw formats: In the uv format, the x-coordinate is the value of u(n) and the y-coordinate is the value of v(n). In the vw format, the x-coordinate is the value of v(n) and the y-coordinate is the value of w(n). And in the uw format, the x-coordinate is the value of u(n) and the y-coordinate is the value of w(n).

Press [CLEAR] to terminate tracing the graph. This also removes the name of the function and the coordinates of the cursor from the screen.

If the name of the sequence and the value of the independent variable n are interfering with your view of the graph when you use TRACE, increase the height of the window by pressing [WINDOW] and decreasing the value of Ymin and increasing the value of Ymax.