How to Do Recursive Sequences on TI-84 Plus CE?

Recursive sequences are a fundamental concept in mathematics, where each term is defined based on the previous term(s). The TI-84 Plus CE graphing calculator is a powerful tool for generating and graphing these sequences. This guide will walk you through the steps to enter and graph recursive sequences on your TI-84 Plus CE, and we'll also introduce a convenient online alternative for those who don't have immediate access to a physical calculator.

Understanding Recursive Sequences

A recursive sequence is defined by a formula that relates each term to one or more of its predecessors. For example, the Fibonacci sequence is defined recursively as:

  • ( F(n) = F(n-1) + F(n-2) ) with initial conditions ( F(0) = 0 ) and ( F(1) = 1 ).

To graph such sequences on the TI-84 Plus CE, you need to follow specific steps to set up your calculator.

Steps to Enter a Recursive Sequence

  1. Set the Calculator to Sequence Mode:

    • Press the [MODE] button.
    • Use the arrow keys to highlight SEQ in the mode menu and press [ENTER].

  2. Access the Y= Editor:

    • Press the [Y=] button to open the Y= editor.

  3. Define the Initial Term:

    • Enter a value for nMin, which is the starting point for your sequence. For example, if your sequence starts at ( n = 1 ), you would enter 1.

  4. Enter the Recursive Formula:

    • In the next line, input the recursive formula for your sequence. For instance, if you are working with an arithmetic sequence defined as ( a(n) = a(n-1) + 3 ), you would enter u(n-1) + 3.

  5. Input the Initial Value:

    • Enter the initial term of the sequence. For example, if the first term is 2, you would enter 2 in the next line.

  6. Graph the Sequence:

    • After entering the necessary information, press the [GRAPH] button to visualize the sequence. The graph will display the points corresponding to each term of the sequence.

Example: Graphing the Fibonacci Sequence

To graph the Fibonacci sequence on your TI-84 Plus CE, follow these steps:

  1. Set the calculator to SEQ mode.
  2. Access the Y= editor.
  3. Set nMin to 1.
  4. Enter the recursive formula: u(n-1) + u(n-2).
  5. Input the initial values: 1 and 1 for the first two terms.
  6. Press [GRAPH] to see the Fibonacci sequence plotted.

Tips for Successful Graphing

  • Ensure that you have entered the correct initial conditions and recursive formulas.
  • Adjust the window settings by pressing [WINDOW] to ensure that all points of the sequence are visible.
  • Use the [TRACE] function to explore individual points on the graph.

Online Alternative

If you don't have immediate access to a physical TI-84 Plus CE calculator, you can use the online TI-84 calculator at TI 84 CALCULATOR ONLINE. This web-based alternative provides the same functionality as the physical calculator, making it perfect for practicing recursive sequences or working on homework when your calculator isn't handy. The online version follows the same steps outlined above and offers the advantage of being accessible from any device with an internet connection.

By following these steps, you can effectively use your TI-84 Plus CE or its online counterpart to work with recursive sequences, enhancing your understanding of this important mathematical concept. Whether you're studying for a test or exploring mathematical patterns, both the physical TI-84 Plus CE and the online calculator are invaluable resources for visualizing and analyzing recursive sequences.