Texas-instruments PLUS TI-89 User Manual download pdf (Page 156)

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Chapter 9: Sequence Graphing 139

09SEQUEN.DOC TI-89/TI-92 Plus: Sequence Graphing (English) Susan Gullord Revised: 02/23/01 10:59 AM Printed: 02/23/01 2:14 PM Page 139 of 14

Chapter 9:

Sequence Graphing

Preview of Sequence Graphing ............................................................ 140

Overview of Steps in Graphing Sequences ......................................... 141

Differences in Sequence and Function Graphing .............................. 142

Setting Axes for Time, Web, or Custom Plots .................................... 146

Using Web Plots...................................................................................... 147

Using Custom Plots................................................................................ 150

Using a Sequence to Generate a Table................................................ 151

This chapter describes how to graph sequences on the

89 / TI

92 Plus

. Before using this chapter, you should be familiar

with Chapter 6: Basic Function Graphing.

Sequences are evaluated only at consecutive integer values. The

two general types of sequences are:

Nonrecursive

— The

th term in the sequence is a function

of the independent variable

Each term is independent of any other terms. In the following

example sequence, you can calculate

u(5)

directly, without

first calculating

u(1)

or any other previous term.

u(n) = 2

for

n = 1, 2, 3, ...

u(n) = 2

gives the sequence

2, 4, 6, 8, 10, ...

Recursive

— The

th term is defined in relation to one or

more previous terms, represented by

u(n

, etc. In

addition to previous terms, a recursive sequence may also be

defined in relation to

(such as

u(n) = u(n

1) + n

In the following example sequence, you cannot calculate

u(5)

without first calculating

u(1)

u(2)

u(3)

, and

u(4)

u(n) = 2

u(n

for

n = 1, 2, 3, ...

Using an initial value of 1:

u(n) = 2

u(n

gives the sequence

1, 2, 4, 8, 16, ...

The number of initial values you need to specify depends on

how deep the recursion goes. For example, if each term is

defined in relation to the previous two terms, you must specify

initial values for the first two terms.

Note: A recursive sequence

can reference another

sequence. For example,

u2(n) = n

+u1(n

1).

n is always a series of

consecutive integers,

starting at any positive

integer or zero.

The first term is undefined

since it has no previous term.

So you must specify an initial

value to use for the first term.

1 2 ... 151 152 153 154 155 156 157 158 159 160 161 ... 622 623

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