Calculator Lessons

Calculating and Graphing Recursive Sequences

Preparing

The first step you must take before calculating reqcursive sequences is to switch you calculator into sequence mode. To do this press the [mode] button and press the down button 3 times. You should be on the mode selection menu. Press the right button until SEQ is selected. Hit [enter]. Your calculator has now been set into sequence mode. To exit the mode menu, press [clear].

Using your calculator in sequence mode

Now that your calculator is in sequence mode, a few things have changed. The [X,T,O,n] button now types n. The [y=] menu now allows you to enter sequences.. Press [y=] to get started. There are a number of entry fields presented to you. nMin should always be 1. u(n), v(n), and w(n) allow you to enter the sequence. In order to type this into the entry field, you will need to use two new keys. You should replace x in the equation with u, v, or w, depending on which entry field you are using. To access these symbols, press [2nd]+[7],[8], or [9]. The symbol that will be typed is shown in blue above their respective number keys.

Programming in the sequence

Now that you know how to enter the sequence, I will walk you through entering the Fibonacci sequence.The Fibonacci sequence is one of the most popular mathematical sequences. The Fibonacci sequence can be represented as x(n) = x(n-1) + x(n-2). Enter the [y=] menu if you aren't already in it. Scroll down to u(n). Press [2nd] and [7] to enter u. Press [(]. Press the [X,T,O,n] button to enter n. Press [-], [1], and then [)] to finish with the 1st term. Press [+] to start on the second term. Again, press [2nd] and [7] to enter u. Press [(]. Press the [X,T,O,n] button to enter n. Press [-], [2], and then [)] to finish with the 1st term. You have now programmed in the sequence, but we aren't finished yet. We will need to enter u(1) and u(2). The 1st and 2nd terms of the Fibonacci sequence are both 1. Enter these now. You have now programmed in the sequence.

Graphing the sequence

To graph the sequence, press [graph]. The sequence may be too large or too small to be viewed on the display. Luckily, there is an easy fix for this. Simply press [zoom]+[0]. Your calculator will automatically zoom in or out to fit the graph on the screen. To return the zoom to normal, press [zoom]+[6].

Calculating values of the sequence

Because you have graphed the sequence, the steps to view a table of it's vlaues are very simple. Press [2nd]+[graph][table]. You will now see a table of the values of the sequence. To increase the "step" size (the difference between each value shown, press [+] and enter your desired step size. Press [enter] to recalculate.