The following lists the steps for entering a sequence into the TI-83 Plus graphing calculator. For the sake of simplicity, this example is for entering the sequence u(n). But what is stated in these steps for u(n) also applies to the sequences v(n) and w(n).

1. Press [MODE] and put the calculator in Sequence mode.

To highlight an item in the Mode menu, use the

keys to place the cursor on the item, and then press [ENTER]. Highlight Seq in the fourth line to put the calculator in Sequence mode. Highlighting Float in the second line displays numbers with as many decimal places as the calculator can handle. If your sequence deals with money, highlight the number 2 in the second line to make the calculator round all numbers to two decimal places.

2. Press [Y=], enter a value for nMin, and press [ENTER].

nMin denotes the first value of the independent variable n in the sequence u(n) and in all other sequences you enter into the calculator. You usually want to set it equal to 1 so your sequences look like {u(1), u(2), u(3), . . .}, {v(1), v(2), v(3), . . .}, and {w(1), w(2), w(3), . . .}.

But if your sequences represent an experiment that starts at “time zero,” you would want to set nMin equal to 0. This way your sequences would look like {u(0), u(1), u(2), . . .} and so on.

To enter the number you’ve chosen for nMin, place the cursor on the number appearing after nMin, press the number keys to enter your new value, and then press [ENTER].

nMin must be set equal to 0 or a positive integer. The calculator isn’t equipped to handle negative values for nMin. Setting nMin equal to something other than 0 or a positive integer results in an error message.

3. Enter the definition of the sequence u(n) and press [ENTER].

To erase an entry that appears after u(n), use the

keys to place the cursor to the right of the equal sign and press [CLEAR]. Then enter your definition for the new sequence.

The sequence function names u, v, and w appear on your keypad in yellow, above [7], [8], and [9], respectively. To enter u, for example, press [2nd][7]. To enter the independent variable n, press

The only variables allowed in the definition of any sequence are these: u(n – 1), u(n – 2), v(n – 1), v(n – 2), w(n – 1), w(n – 2), and n. For example, defining u(n) = v(n) + 1 results in an error message.

4. Enter the value of u(nMin) and press [ENTER].

u(nMin) is left blank, set equal to the first term in the sequence u(n), or set equal to the first two terms in u(n). It all depends of how the sequences u, v, and w are defined.

The following tells you what value to assign to u(nMin) and how it’s entered in the calculator:

• u(nMin) can be left blank if none of the sequences u, v, or w use u(n – 1) or u(n – 2) in their definitions. If u(nMin) has previously been assigned a value, you can get rid of that value by using the

keys to place the cursor after the equal sign, pressing [CLEAR] to erase it, and then blanking it by pressing [ENTER].

• u(nMin) is set equal to the first term in the sequence u(n) if any of the sequences u, v, or w use u(n – 1) in their definitions, but none of them use u(n – 2). To set u(nMin) equal to the first term in the sequence u(n), use the

keys to place the cursor after the equal sign, then use the number keys to enter the value you want to assign u(nMin), and press [ENTER]. As you enter this number, the calculator automatically erases any previous value assigned to u(nMin); after you press [ENTER], the calculator automatically places curly braces around the number you just entered.

• u(nMin) is set equal to the first two terms in the sequence u(n) if any of the sequences u, v, or w use u(n – 2) in their definitions. And to complicate matters, these terms must be entered in reverse order, and you must supply the curly braces.

You enter these terms after the equal sign for u(nMin) by keying in: {second term in u(n), first term in u(n)}. The curly braces are entered into the calculator by pressing [2nd][ ( ] and [2nd][ ) ].

If you’re ever in doubt about how to set u(nMin), you can never go wrong by setting it equal to the first two terms in the sequence u(n). However, it’s not always mathematically easy to find these two terms.

In the figure, u(nMin) is left blank because none of the sequences u, v, or w used u(n – 1) or u(n – 2) in their definitions. v(nMin) is set equal to the first term in v(n) because v(n) used v(n – 1) in its definition. In this example v(nMin) was assigned the value of 5.

Because u(n) used w(n – 2) in its definition, w(nMin) is set equal to the first two terms in w(n), listed in reverse order.