body{margin:0;} noscript{z-index: 10000; position: fixed; display: block; height: 100%; width: 100%; background: #fff;} noscript .fa{font-size: 40px; display:block; color: #daa520;} noscript div{margin-top: 6%; padding-left: 20px; padding-right: 20px; text-align: center;} ! You must have JavaScript enabled to use this site.

Big Ideas Math Integrated III

BI

Big Ideas Math Integrated III View details

5. Using Recursive Rules with Sequences

Continue to next subchapter

Exercise 4 Page 389

What does a recursive rule include?

See solution.

Practice makes perfect

To define a sequence recursively, there are two things to consider.

The beginning term(s).
The recursive equation.

A sequence can have one beginning term or more than one. After we identify the beginning term(s), we can write a recursive equation. This equation tells how

a_{n}

is related to one or more preceding terms. The beginning term(s) and a recursive equation define a sequence recursively.

Extra

Sequence

Let

a_{1} = 1

and

a_{2} = 2

be the beginning terms of the sequence.

a_{1} = 1 and a_{2} = 2

We will let

a_{n} = a_{n - 2} + 0.5 a_{n - 1}

be the recursive equation.

a_{n} = a_{n - 2} + 0.5 a_{n - 1}

The beginning terms and the recursive equation define a recursive rule.

a_{1} a_{2} a_{n} = 1 = 2 = a_{n - 2} + 0.5 a_{n - 1}

This recursive rule defines a sequence.

1, 2, 2, 3, 3.5, \dots

Subchapter links

Communicate Your Answer p.389

Monitoring Progress p.390-394

Exercises p.395-398