GDC skill: define sequence by recurrence relation

Generating recurrence sequences (recursive formulas) on a TI-Nspire can be done using the Lists & Spreadsheet application for tables of values or the Graphing application for visual representation.
Here are the primary methods to generate recurrence sequences:

Method 1: Using Lists & Spreadsheet (Best for Tables)

This method is ideal for generating a list of terms based on previous terms, such as the Fibonacci sequence (\(u_{n}=u_{n-1}+u_{n-2}\)). 

1. Open a New Application: Open the Lists & Spreadsheet app.
2. Generate Sequence: Move to the formula cell (the cell below 'A') and press [MENU] \(\rightarrow \) Data \(\rightarrow \) Generate Sequence.
3. Configure the Dialog Box:
   1. Formula: Enter your recursive formula using \(u(n-1)\) for the previous term and \(u(n-2)\) for the term before that. For example, for Fibonacci, enter u(n-2)+u(n-1).
   2. Initial Terms: Define the starting values separated by commas (e.g., 1,1).
   3. \(n_{0}\): The starting index, usually 1
   4. \(nMax\): How many terms you want to generate (e.g., 10).
   5. \(nStep\): Set to 1.
4. Generate: Press [ENTER].

Method 2: Using the Calculator Page (Iterative Method)

This method is useful for quickly finding a specific term by repeatedly pressing Enter.

1. Enter Initial Term: Type the first term (e.g., 3) and press [ENTER].
2. Define Rule: Type the formula for the next term using [2nd] [ANS] to represent the previous term. For example, if the rule is \(a_{n}=2a_{n-1}+1\), type 2*Ans + 1.
3. Calculate: Press [ENTER] repeatedly to generate subsequent terms.

1. Open Graph: Open the Graph app.
2. Change Graph Type: Press [MENU] \(\rightarrow \) Graph Type \(\rightarrow \) Sequence \(\rightarrow \) Sequence.
3. Change Graph Type: Press [MENU] \(\rightarrow \) Graph Type \(\rightarrow \) Sequence \(\rightarrow \) Sequence.
   1. Enter the formula in \(u1(n)=\dots \)
   2. Enter the initial value in \(u1(n_{0})=\dots \)
4. Graph and Table: Press [ENTER] to plot the graph. Press [CTRL] [T] to view the table of values.

You can follow the link https://www.youtube.com/watch?v=FnklA-Iz6Uc to watch a video-demonstration of how TI-nSPIRE can be used to generate a sequence defined by a recurrence relation.