Here are some examples showing how to graph sequences on the TI-83 Plus, the TI-85, and the TI-89. For these examples, take

We will attempt to plot this sequence for n = 0 to 50.

Click on the appropriate link to jump to the example using the TI-83 Plus, the TI-85, or the TI-89.

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On the TI-83 Plus, there are (at least) two ways to plot sequences. One involves drawing a graph in Sequence mode (Seq on the MODE screen); the other involves drawing a graph in Parametric mode (Par on the MODE screen). Strangely enough, for non-recursive sequence definitions, the Parametric option is both easier to use and more flexible. We'll demostrate both options here.

Sequence Mode on the TI-83    [Jump to Parametric Mode]

To begin, we press the [MODE] key and use the arrow keys and the [ENTER] key to highlight Seq and Dot.

The resulting MODE screen looks like this:

Next we press the [Y=] key to get to the function definition screen. This will look different from the usual Y= screen, but functions and limits are entered in pretty much the same way. We set the variable nMin to zero, and set u(n) to the formula for the n^th term of our sequence. When we are finished, the screen looks like this:

(We used the [X,T,Θ,n] key to get the italic n.)

Next we press [WINDOW] to bring up the WINDOW screen. We want to plot our sequence for n going from 0 to 50, so we set nMin to 0 and nMax to 50.

We want to start plotting points at n = 0, so we'd like to set PlotStart to 0. However, the calculator will not let us do that. The smallest value of PlotStart it will accept is 1. So we set PlotStart to 1.

We want to plot a point for every integer value of n, so we set PlotStep to 1.

Finally, we set Xmin, Xmax, Xscl, Ymin, Ymax, and Yscl to create a window of a useful size (say, x from 0 to 50 and y from -1 to 3) and to place tickmarks at useful intervals (say, every 10 units along the x-axis and every one unit along the y-axis). Here's what the screen looks like when we finish (we have scrolled down so that the top few lines aren't visible):

We press the [GRAPH] to draw the picture. It looks like this:

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Parametric Mode on the TI-83

The idea here is to use parametric plotting to plot points with coordinates (t, a_t) as t goes from 0 to 50.

To begin, we press the [MODE] key and use the arrow keys and the [ENTER] key to highlight Par and Dot.

The resulting MODE screen looks like this:

Next we press the [Y=] key to get to the function definition screen. We set X_1T equal to T and Y_1T equal to our formula for a_T. When we are finished, the screen looks like this:

(We used the [X,T,Θ,n] key to get the variable T.)

Next we press [WINDOW] to bring up the WINDOW screen. We want to plot our sequence for T going from 0 to 50 by ones, so we set Tmin to 0, Tmax to 50, and Tstep to 1.

We set Xmin, Xmax, Xscl, Ymin, Ymax, and Yscl to create a window of a useful size (say, x from 0 to 50 and y from -1 to 3) and to place tickmarks at useful intervals (say, every 10 units along the x-axis and every one unit along the y-axis). Here's what the screen looks like when we finish (only the top eight lines of the screen are visible):

We press the [GRAPH] to draw the picture. It looks like this:

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The TI-85, unlike the TI-83 and the TI-89, doesn't seem to support a Sequence graphing mode (the SeqG setting on the GRAPH FORMT screen is something different), so we are forced to use the parametric plotting mode to plot sequences.

To begin, we press [2nd][MODE] and use the arrow keys and the [ENTER] key to highlight Param on the MODE screen.

We then press [GRAPH] to bring up the graphing menu. Since we're in parametric mode, the first item on the menu is E(t)= instead of the more familiar y(x)=.

We press [F1] to get to the E(t)= screen. Our goal is to plot a sequence of points whose coordinates are (t, a_t). To do this, we want to set xt1 to t and yt1 to our formula for a_t.

Using the arrow and other editing keys, we enter the value t for xt1 and the string

(2t+(-1)^t)/(t+3)

for yt1. (We use the [F1] key to get the variable t.) When we're finished, the screen looks like this:

Next we type [EXIT] to get back to the primary GRAPH menu, and [MORE], to get to the part of the menu containing the option FORMT. We type [F3] to bring up the FORMAT screen. We use the arrow keys and the [ENTER] to highlight DrawDot.

Next we type [F2] to get the RANGE menu. We want the variable t to go from 0 to 50 by ones, so we set tMin to 0, tMax to 50, and tStep to 1.

We set xMin, xMax, xScl, yMin, yMax, and yScl to create a window of a useful size (say, x from 0 to 50 and y from -1 to 3) and to place tickmarks at useful intervals (say, every 10 units along the x-axis and every one unit along the y-axis). Here's what the screen looks like when we finish (only the bottom eight lines of the screen are visible):

Finally, we press [F5] to draw the graph. Here is the result:

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On the TI-89, there are (at least) two ways to plot sequences. One involves drawing a graph in SEQUENCE mode; the other involves drawing a graph in PARAMETRIC mode. For non-recursive sequence definitions, the Parametric option is both easier to use and more flexible. We'll demostrate both options here.

Sequence Mode on the TI-89    [Jump to Parametric Mode]

To begin, we press the [MODE] key to call up the mode menu, then the right arrow key to bring up the sub-menu of graphing modes. We use the arrow keys to highlight SEQUENCE.

We press [ENTER] twice to return to the home screen. We then press [(diamond)][F1] to go to the Y= screen. (The symbol "(diamond)" is the green diamond key, just under the [2nd] key.) On the Y= page, we set u1 to the formula for the n^th term of our sequence by highlighting the u1= line and typing in

(2*n+(^-1)^n)/(n+3)

When we finish, the screen looks like this:

Next we use the up arrow key to highlight the formula again, and press [2nd][F1] to call up the Style menu. We use the arrow keys to highlight to highlight 2: Dot.

We then press ENTER to return to the Y= screen, and then [(diamond)][F2] to bring up the WINDOW screen. We want to plot our sequence for n going from 0 to 50, so we set nmin to 0 and nmax to 50.

We want to start plotting points at n = 0, so we'd like to set plotStrt to 0. However, the calculator will not let us do that. The smallest value of plotStrt it will accept is 1. So we set plotStrt to 1.

We want to plot a point for every integer value of n, so we set plotStep to 1.

Finally, we set xmin, xmax, xscl, ymin, ymax, and yscl to create a window of a useful size (say, x from 0 to 50 and y from -1 to 3) and to place tickmarks at useful intervals (say, every 10 units along the x-axis and every one unit along the y-axis). Here's what the screen looks like when we finish (the bottom line, yscl=1., is only partly visible):

We press [(diamond)][F8] to draw the picture. It looks like this:

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Parametric Mode on the TI-89

The idea here is to use parametric plotting to plot points with coordinates (t, a_t) as t goes from 0 to 50.

To begin, we press the [MODE] key to call up the mode menu, then the right arrow key to bring up the sub-menu of graphing modes. We press use the arrow keys to highlight PARAMETRIC.

We press [ENTER] twice to return to the home screen. We then press [(diamond)][F1] to go to the Y= screen. (The symbol "(diamond)" is the green diamond key, just under the [2nd] key.) On the Y= page, we want to set xt1 equal to t and yt1 equal to our formula for the t^th term of the sequence. To do this, we first highlight the xt1= line and type [T][ENTER]. Then we highlight the yt1= line and type in the formula

(2*t+(^-1)^t)/(t+3)

(The variable t is on the [T] key.) When we finish, the screen looks like this:

Next we use the up arrow key to highlight either the xt1 or yt1 line, and press [2nd][F1] to call up the Style menu. We use the arrow keys to to highlight 2: Dot.

We then press ENTER to return to the Y= screen, and then [(diamond)][F2] to bring up the WINDOW screen. We want to plot our sequence for t going from 0 to 50 by ones, so we set tmin to 0, tmax to 50, and tstep to 1.

We set xmin, xmax, xscl, ymin, ymax, and yscl to create a window of a useful size (say, x from 0 to 50 and y from -1 to 3) and to place tickmarks at useful intervals (say, every 10 units along the x-axis and every one unit along the y-axis). Here's what the screen looks like when we finish:

We press [(diamond)][F8] to draw the picture. It looks like this:

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