Texas Instruments TI-82 User Manual

25
G
RAPHING
T
ECHNOLOGY
G
UIDE
: TI-82
Copyright © Houghton Mifflin Company. All rights reserved.
2.7 Sequences
2.7.1 Iteration with the ANS Key: The ANS feature permits you to perform iteration, the process of evaluating a
function repeatedly. As an example, calculate
1
3
n −
for n = 27. Then calculate
1
3
n −
for n = the answer to the
previous calculation. Continue to use each answer as n in the next calculation. Here are keystrokes to accomplish
this iteration on the TI-82 calculator (see the results in Figure 2.70). Notice that when you use ANS in place of n in a
formula, it is sufficient to press ENTER to continue an iteration.
Iteration Keystrokes Display
1
27 ENTER
27
2
(2nd Ans – 1) ÷ 3 ENTER
8.666666667
3
ENTER
2.555555556
4
ENTER
.5185185185
5
ENTER
-.1604938272
Press ENTER several more times and see what happens with this iteration. You may wish to try it again with a
different starting value.
Figure 2.70: Iteration
2.7.2 Arithmetic and Geometric Sequences: Use iteration with the ANS variable to determine the n-th term of a
sequence. Enter the first term 7, then start the progression with the recursion formula, 2nd ANS + 4 ENTER. This
yields the 2nd term, so press ENTER sixteen more times to find the 18th term. For a geometric sequence whose
common ratio is 4, start the progression with 2nd ANS × 4 ENTER.
You can also define the sequence recursively with the TI-82 by selecting Seq in the MODE menu (see Figure 2.1).
Once again, let’s find the 18th term of an arithmetic sequence whose first term is 7 and whose common difference is
4. Press MODE ▼ ▼ ▼ ► ► ► ENTER 2nd QUIT. Then press Y= to edit either of the TI-82’s two sequences,
u
n
and v
n
. Make u
n
= u
n – 1
+ 4 by pressing 2nd u
n – 1
+ 4. Now make u
1
= 7 by pressing WINDOW and setting
UnStart = 7 and nStart = 1 (because the first term is u
1
where n = 1). Press 2nd QUIT to leave this menu and
return to the home screen. To find the 18th term of this sequence, calculate u
18
by pressing 2nd Y-
VARS
4 1 ( 18 )
ENTER (see Figure 2.71).

Texas Instruments TI-82 Specifications

General

Type	Graphing calculator
Processor	Zilog Z80, 6 MHz
RAM	28 KB
ROM	128 KB
Programming	TI-BASIC
Display	Monochrome LCD
Power	4 AAA batteries

Summary

2.1 Getting Started with the TI-82

Basics

Initial setup, power, contrast, and display settings for the TI-82 calculator.

Editing

How to edit previous calculations and correct entries using cursor keys.

The MATH Menu

2.2 Functions and Graphs

Evaluating Functions

Entering and evaluating functions for calculations and tables.

Functions in a Graph Window

TRACE

ZOOM

Techniques for enlarging or reducing graph views for better analysis.

Relative Minimums and Maximums

Finding and approximating local extrema of functions on a graph.

2.3 Solving Equations and Inequalities

Intercepts and Intersections

Locating x-intercepts and points where graphs cross.

Solving Equations by Graphing

Solving Systems by Graphing

2.4 Trigonometry

Degrees and Radians

Setting angle modes (degrees/radians) for trigonometric functions.

2.5 Scatter Plots

Entering Data

Plotting Data

Regression Line

Calculating and graphing the line of best fit for data.

Exponential Growth Model

2.7 Sequences

Iteration with the ANS Key

Repeating calculations using the ANS variable.

Arithmetic and Geometric Sequences

2.10 Programming

Entering a Program

Creating and writing programs on the TI-82.

Executing a Program

Running stored programs on the calculator.

2.11 Differentiation

Limits

Numerical Derivatives

Calculating numerical approximations of derivatives.

Newton's Method

2.12 Integration

Approximating Definite Integrals

Numerically approximating definite integrals.

Areas