13 2 recursive definitions

Objectives:

1. Write and use recursive sequence

definitions.

What comes next?3, 7, 11, 15, …

How do you know?

Recursive DefinitionsGive value of tn in terms of previous

term tn – 1.

Contain two parts:

Initial condition

tells where it starts

Recursion formula

tells how each term is related to

previous term

Examplet1 = 3

tn = 2tn – 1 + 1

You Try!Find the first 5 terms:

t1 = 10

tn = tn – 1 + n

ExampleGive a recursive definition for:

2, 6, 18, 54, 162, …

1, 2, 6, 24, 120, 720, …

You Try!Give a recursive definition for:

81, 27, 9, 3, …

Recursive vs. Explicit23, 20, 17, 14, …

Recursive definition: t1 = 23

tn = tn – 1 – 3

Explicit definition: tn = 26 – 3n

Finding Explicit Definitions Find the first 5 terms of

t1 = 3

tn = tn – 1 + 4

Write an explicit definition.

You Try!Write an explicit definition for

t1 = 8

tn = ½ tn – 1

ApplicationsThe population of some country grows

two ways:

1. Annual growth of 1%

2. 20,000 people immigrate each year

If the population is now 5,000,000, what

will it be in 4 years?

13 2 recursive definitions

Education

Transcript of 13 2 recursive definitions

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