How to Graph Sequences on the TI-83 Plus
In spite of the power of the TI-83 Plus graphing calculator, it’s rather limited when dealing with sequence functions. However, after you have entered the sequence functions into the calculator, you can use the following steps to graph the sequences:
Turn off any Stat Plots that you don’t want to appear in the graph of your sequences.
The first line in the Y= editor tells you the graphing status of the Stat Plots.
If Plot1, Plot2, or Plot3 is highlighted, then that Stat Plot will be graphed along with the graph of your sequences. If it’s not highlighted, it won’t be graphed. In this example, Plot1 will be graphed along with the sequences.
To turn off a highlighted Stat Plot in the Y= editor, use the
keys to place the cursor on the highlighted Stat Plot and then press [ENTER]. If you want to graph the Stat Plot later on, use this same process to rehighlight it.
When you’re graphing sequences, Stat Plots that are turned on when you don’t really want them graphed cause problems. The most common problem is the ERR: INVALID DIM error message, which gives you precious little insight into what’s causing the problem. So if you aren’t planning to graph a Stat Plot along with your sequences, make sure all Stat Plots are turned off.
Press [2nd][ZOOM] to access the Format menu.
Set the format for the graph in the first line of the Format menu by placing the cursor on the desired format and then pressing [ENTER].
Press [WINDOW] to access the Window editor.
After each of the first four window variables, enter a numerical value that is appropriate for the sequences you’re graphing. Press [ENTER] after entering each number.
If you know the dimensions of the viewing window required for your graph, go ahead and assign numerical values to the appropriate variables in the Window editor and advance to Step 8. If you don’t know the minimum and maximum y values required for your graph, the next step tells you how to get the calculator to find them for you.
Press [ZOOM] to access ZoomFit.
After you have assigned values to nMin, nMax, PlotStart, and PlotStep, ZoomFit determines appropriate values for Xmin, Xmax, Ymin, and Ymax and graphs your sequences. ZoomFit graphs the sequences in the smallest possible viewing window, however, and it won’t assign appropriate values to Xscl and Yscl.
If you like the way the graph looks, then you can skip the remaining steps. If you’d like to spruce up the graph, Step 7 gives you some pointers.
Press [WINDOW] and adjust the values assigned to the X and Y settings. Press [ENTER] after entering each new number.
Here’s how to readjust the viewing window after using ZoomFit:
Xmin: If you want to see the y-axis on your graph, set Xmin equal to 0.
Xmax: If you’re interested in seeing a more detailed graph of the beginning of the sequence, decrease the value of Xmax.
Xscl: Set this equal to a value that doesn’t make the x-axis look like railroad tracks — that is, an axis with far too many tick marks. Twenty or fewer tick marks makes for a nice looking axis.
Ymin and Ymax: If you don’t want the graph to hit the top and bottom of the screen, decrease the value assigned to Ymin and increase the value assigned to Ymax. If you want to see the x-axis on the graph, assign values to Ymin and Ymax so that zero is strictly between these two values.
Yscl: Set this equal to a value that doesn’t make the x-axis look like railroad tracks (too many tick marks). Fifteen or fewer tick marks is a nice number for the y-axis.
Press [GRAPH] to regraph the sequences.
When you’re graphing sequences, if you get the ERR: INVALID error message and then select the Goto option, the calculator sends you to the definition of the problem sequence that you placed in the calculator.
More often than not, however, the true location of the problem is in the way you defined u(nMin), v(nMin), or w(nMin), and not in the way you defined the sequence (as the calculator leads you to believe).
For example, if w(n) = u(n – 2) + v(n – 1) and the calculator places the cursor after u(n – 2) when you select the Goto option, then the problem is most likely caused by not setting u(nMin) equal to the first two terms in u(n).