# How to Enter a Sequence on the TI-83 Plus

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*).

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**2**in the second line to make the calculator round all numbers to two decimal places.Press [Y=], enter a value for

*n*Min, and press [ENTER].denotes the first value of the independent variable*n*Min*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**equal to 0. This way your sequences would look like {u(0), u(1), u(2), . . .} and so on.*n*MinTo enter the number you’ve chosen for

, place the cursor on the number appearing after*n*Min, press the number keys to enter your new value, and then press*n*Min**[ENTER]**.must be set equal to 0 or a positive integer. The calculator isn’t equipped to handle negative values for*n*Min. Setting*n*Minequal to something other than 0 or a positive integer results in an error message.*n*MinEnter the definition of the sequence u(

*n*) and press [ENTER].To erase an entry that appears after u(

*n*), use thekeys 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*, pressThe 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.Enter the value of u(

*n*Min) and press [ENTER].**u(**is left blank, set equal to the first term in the sequence u(*n*Min)*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(**and how it’s entered in the calculator:*n*Min)**u(**can be left blank if none of the sequences*n*Min)**u**,**v**, or**w**use u(*n*– 1) or u(*n*– 2) in their definitions. If**u(**has previously been assigned a value, you can get rid of that value by using the*n*Min)keys to place the cursor after the equal sign, pressing

**[CLEAR]**to erase it, and then blanking it by pressing**[ENTER]**.**u(**is set equal to the first term in the sequence u(*n*Min)*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(**equal to the first term in the sequence u(*n*Min)*n*), use thekeys to place the cursor after the equal sign, then use the number keys to enter the value you want to assign

**u(**, and press*n*Min)**[ENTER]**. As you enter this number, the calculator automatically erases any previous value assigned to**u(**after you press*n*Min);**[ENTER]**, the calculator automatically places curly braces around the number you just entered.**u(**is set equal to the first two terms in the sequence u(*n*Min)*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(**by keying in: {second term in u(*n*Min)*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(**, you can never go wrong by setting it equal to the first two terms in the sequence u(*n*Min)*n*). However, it’s not always mathematically easy to*find*these two terms.

In the figure,

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

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