Math 30P Exponents Logarithms Sequences Series Regression/Recursive Interest Growth Richter/PH Prerequisite Skills
To Clear All Lists: [2nd] [+] 4: ClearAllLists
Window settings: [ZOOM], 6:Standard
Make sure you use the [ () ] key for the values that are negative.
Quadratic Regression: 
Exponential Regression: 

This is the data we for the quadratic regression.

This is the data for the exponential regression.


[STAT]  select EDIT 1: Edit
Enter Data into you calculator:
[STAT]  select CALC 5: QuadReg
Add: [ 2nd ] [1] [ , ] [ 2nd ] [2] [ , ] [VARS] YVars 1: Function FUNCTION 1: Y1 [ENTER] [ENTER] [ Y= ] [GRAPH] Check to see if the points from the table fit the quadratic regression. First change the settings to plot a scatterplot graph of the data in the original table. [ 2nd ] [Y = ] [ENTER ] [GRAPH] 
[STAT]  select EDIT 1: Edit
Enter Data into you calculator:
[STAT]  select CALC 0: ExpReg
Add: [ 2nd ] [1] [ , ] [ 2nd ] [2] [ , ] [VARS] YVars 1: Function FUNCTION 1: Y1 [ENTER] [ENTER]
[ Y= ] [GRAPH] Not Available at this time.
Check to see if the points from the table fit the exponential regression. First change the settings to plot a scatterplot graph of the data in the original table. [ 2nd ] [Y = ] [ENTER ] [GRAPH] Not Available at this time. 
In the above example, the regression equation was placed in Y1 at time the regression is made.
[ENTER] 
Alternative is to place the regression in Y1 after the regression is made.Following: [ENTER] Place the regression data into Y1: [ Y = ] [ VARS ] 5: Statistics EQ 1: RegEQ 
Another copy: TI83+ Instructions
For example, t_{n} = t_{n1} + n, where t_{1} = 5, is a recursive formula.
A recursive formula that generates a sequence is dependent on one or more previous terms. It is not defined explicitly in terms of n. Since it is dependent on at least one previous term, at least one of the values of the terms must be stated. If t_{n} is the nth term, then the previous term is t_{n1}.
Example 1: Arithmetic Sequence List the first 7 terms for the a sequence with the recursive formula where t_{1} = 1, Create a table of values and graph the sequence. Solution Terms: 1, 5/2, 4, 11/2, 7, 17/3, 10 Because you are working with sequences, set your calculator to Seq mode and Dot mode (as shown). To generate the table of values for a sequence or to graph the sequence, you need to enter the function, which is the general term or explicit formula. To enter the function , where t_{1} = 1, press the following keystrokes: Since t_{1} = 1, enter the minimum value for u(nMin) as 1. Press the following keystrokes: Press to see the points of the sequence plotted. If there is no graph, you will have to adjust the window settings (domain and range). You may want to check the table of values to determine a suitable domain and range. To do this, press [ TABLE ]. 
Example 2: Geometric Sequence List the first 7 terms for the a sequence with the recursive formulawhere t_{1} = 1, Create a table of values and graph the sequence. Compare the sequences given in Example 1 and Example 2. Solution Terms: 1, 3/2, 9/4, 27/8, 7, 81/16, 243/64 Let , where t_{1} = 1, be the function represented by v(n). Press , select “v(n),” and enter the following: Now, you can display the table by pressing [ TABLE ] or you can display the graph of both sequences by pressing . To compare and contrast, you may want to change the window settings.

Parts of this work has been adapted from a Math 30 Pure learning resource originally produced and owned by Alberta Education
Math 30P Exponents Logarithms Sequences Series Regression Interest Growth Richter/PH Prerequisite Skills