TI-82 Users Guide #2

Generating a sequence

The / button will allow you to create and store lists of values and sequences of numbers. We will begin by making some simple lists on the home screen, then we will move to some simple mathematical operations with lists.

THE SEQUENCE COMMAND: To creat a list of values from the home screen press <2nd > and / which calls the List menus. The 5th command is the sequence command. When you press 5 or enter, the home screen will display "seq(".

The sequence command needs five elements to work. To help you see how it works, try each of these examples.

 To display Enter the command The integers from 1 to 10 Seq(x,x,1,10,1) The multiples of 3 from 9 to 39 Seq(3x,x,3,13,1) Or seq(x,x,9,39,3) The cubes of the numbers from 4 to 8 Seq(x^3,x,4,8,1) The cubes of the EVEN numbers from 4 to 8 Seq(x^3,x,4,8,2)

To see some of the longer sequences, or the ones with decimal values you will need to use the right arrow to scroll out Notice that each command has five parts, and in all of ours, the second part has been the variable x. This will usually be true for most of your early efforts, but you can use other variables. The First thing in the parentheses is a definition of the numbers to be generated, the function rule. In the first command above, all we wanted was to use the values of x, and in the last, we wanted to use the cube of the value of x. The last three parts of the function tell the calculator what values to use in the expression for x. The three commands can be considered as "from" , "to" , and "counting by". I read the commands like this:

Seq(x,x,1,10,1) says print x, as x goes from 1 to 10 counting by 1.

Seq(x^3,x,4,8,2) says print x^3 as x goes from 4 to 8 counting by 2.

You might want to see how a command like seq(4x, x, 4,8,3) would work. Can you see why there are only two output values? It is NOT necessary that the "to", "from" , or "count by" values be integers. You can use something like seq(3*x, x, 1.5, 2.5, .25) . You can also use fractions, and any of the Ti constants such as Pi or Euler's number, and the special operator functions like "Int" or "Abs".

Experiment and see if you can produce the following:

1. Generate the odd numbers from 15 to 21
2. Generate the square of the first five odd numbers
3. Generate the powers of 3 from 3 to 243
4. Generate the first eight triangular numbers (triangular numbers are given by n(n+1)/2… they are 1,3,6,10,15…
5. Generate the annual value each year if \$500 is invested at 12% compound interest for five years.
6. Simulate ten rolls of a die by generating a list of ten integers in the interval from one to six.
7. Generate a list of the sines of angles which are multiples of 90 degrees..from zero to 720 degrees (be sure you are in degree mode)

USING THE SEQUENCE COMMAND TO CREATE A LIST OF RANDOM NUMBERS
By using the random command nested inside the sequence command, you can send a list of random numbers, or random integers, to one of the lists. Here is a command that will simulate ten rolls of a single die and store the results in List one.
Seq(int(rand*6+1),x,1,10,1) -> L1
The same command can be made a little simpler in the TI-83 by using the "randInt" command. Of course, you could repeat this with list L2 and and then use the command L1+L2 -> L3 and get a list of ten rolls of TWO dice added together. Try repeating some of projects in the first exercise and storing the results in a list

If you have these all figured out, go on to the next unit where we will teach you how to do some mathematical operations with lists, such as finding the largest number, or the mean of the list or the sum of the list or… …. So much math, so little time….. hurry back.

CAREFUL… WE STORED THE ANSWERS DOWN HERE… DON'T LOOK BEFORE YOU REALLLLLLY TRY TO ANSWER THE QUESTIONS

We have listed at least one way to do each of these, there is almost always more than one way to do it. Can you find a shorter way to do these…send it to me and I'll add to my list and give you credit.

1. lots of ways to do this seq(x,x,15,21,2) or seq(2x+1,x,7,10,1)
2. Another one with lots of answers seq(x^2,x,1,9,2) or seq((2x+1)^2,x,0,4,1)
3. Seq(3^x,x,1,5,1)
4. Seq(n*(n+1)/2,n,1,8,1) … Ok , you can also use x, but we wanted to do at least one that had another variable in it.
5. Seq(500(1.12)^x,x,0,5,1) we had it print the initial \$500, If you started with one you would only get the amount at the end of each of the five years.
6. Seq(Int(6*rand+1),x,1,10,1) notice there is NO VARIABLE in the expression… it only exists to count how many times we "rolled".
7. Seq(sin(x),x,0,720,90) or you could do seq(sin(90x),x,0,8,1)