<p>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. <br>Here are the primary methods to generate recurrence sequences:</p>
<p><strong>Method 1: Using Lists & Spreadsheet (Best for Tables) </strong></p>
<p>This method is ideal for generating a list of terms based on previous terms, such as the Fibonacci sequence (\(u_{n}=u_{n-1}+u_{n-2}\)). </p>
<ol class="num-list"><li><div class="list-item-paragraph">Open a New Application: Open the Lists & Spreadsheet app.</div></li><li><div class="list-item-paragraph">Generate Sequence: Move to the formula cell (the cell below 'A') and press [MENU] \(\rightarrow \) Data \(\rightarrow \) Generate Sequence.</div></li><li><div class="list-item-paragraph">Configure the Dialog Box:</div><ol class="i-list"><li><div class="list-item-paragraph">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).</div></li><li><div class="list-item-paragraph">Initial Terms: Define the starting values separated by commas (e.g., 1,1).</div></li><li><div class="list-item-paragraph">\(n_{0}\): The starting index, usually 1</div></li><li><div class="list-item-paragraph">\(nMax\): How many terms you want to generate (e.g., 10).</div></li><li><div class="list-item-paragraph">\(nStep\): Set to 1.</div></li></ol></li><li><div class="list-item-paragraph">Generate: Press [ENTER]. </div></li></ol>
<p><strong>Method 2: Using the Calculator Page (Iterative Method)</strong></p>
<p>This method is useful for quickly finding a specific term by repeatedly pressing Enter. </p>
<ol class="num-list"><li><div class="list-item-paragraph">Enter Initial Term: Type the first term (e.g., 3) and press [ENTER].</div></li><li><div class="list-item-paragraph">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.</div></li><li><div class="list-item-paragraph">Calculate: Press [ENTER] repeatedly to generate subsequent terms. </div></li></ol>
<div class="titled-block"><div class="titled-block-title"><strong>Method 3: Using Graphing App (Sequence Mode)</strong></div><p>This method allows you to visualize the sequence. </p></div>
<ol class="num-list"><li><div class="list-item-paragraph">Open Graph: Open the Graph app.</div></li><li><div class="list-item-paragraph">Change Graph Type: Press [MENU] \(\rightarrow \) Graph Type \(\rightarrow \) Sequence \(\rightarrow \) Sequence.</div></li><li><div class="list-item-paragraph">Change Graph Type: Press [MENU] \(\rightarrow \) Graph Type \(\rightarrow \) Sequence \(\rightarrow \) Sequence.</div><ol class="abc-list"><li><div class="list-item-paragraph">Enter the formula in \(u1(n)=\dots \)</div></li><li><div class="list-item-paragraph">Enter the initial value in \(u1(n_{0})=\dots \)</div></li></ol></li><li><div class="list-item-paragraph">Graph and Table: Press [ENTER] to plot the graph. Press [CTRL] [T] to view the table of values. </div></li></ol>
<p style="font-size: 0.75rem">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.</p>

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 (\(u_{n}=u_{n-1}+u_{n-2}\)). 

Open a New Application: Open the Lists & Spreadsheet app.

Generate Sequence: Move to the formula cell (the cell below 'A') and press [MENU] \(\rightarrow \) Data \(\rightarrow \) Generate Sequence.

**Method 2: Using the Calculator Page (Iterative Method)**

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

Enter Initial Term: Type the first term (e.g., 3) and press [ENTER].

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.

Calculate: Press [ENTER] repeatedly to generate subsequent terms. 

This method allows you to visualize the sequence. 

**Method 3: Using Graphing App (Sequence Mode)**

Change Graph Type: Press [MENU] \(\rightarrow \) Graph Type \(\rightarrow \) Sequence \(\rightarrow \) Sequence.

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.

Recurrence Relations and Summation

International Baccalaureate Higher Level Mathematics

GDC skill: define sequence by recurrence relation

GDC skill: define sequence by recurrence relation