13 2 recursive definitions
TRANSCRIPT
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
t2 =
t3 =
t4 =
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?
