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Online Tutorial -
CG50: How to Generate Sequences

Video Transcript

In this tutorial we'll be looking at generating sequences using a term to term rule that's inductively. Using the answer key can be useful, as can the recursion mode, so this tutorial looks at both these methods. To work along with this tutorial, you may find it easiest to reset the calculator before starting so that your screen matches the one in the video.

Choose run mode. Type 11 and execute. Type add five and the display shows, answer plus five. Press execute as many times as you need. If you go too far, you can always scroll back up the list of answers to see the previous ones. In the next example, a term to term rule is given algebraically. So from the main menu, recursion mode is used to generate the sequence. As you start to type the formula AN appears for F2 to be used in the formula.

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We want the first to the eighth terms of the sequence. Choose a 0 for the first term and enter 10 and execute. Go to the table for the list of values. Notice that up to three sequences can be shown side by side. Iteration can be used as the basis of a numerical method for solving equations. And recursion mode can both create and graph the sequence. Exit and scroll up to delete the existing formula. Type the iterative formula, using AN for the variable XN. choose settings 0 and 10 for the number of terms and Pi over four for A0. If you want to see the cobweb diagram as well, enter Pi over four for anStr as the starting point of the diagram. Go to the table to see the sequence and you can scroll across for more decimal places and down to see later values. It's often clearer to see the sequence as a cobweb graph. To do this click web graph and then execute to bring up the start value. Execute again to see the cobweb appear step by step.

Use F6 or exit to return to the list of values and now graph plot will give a different graph showing AN against N.

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