Transcript 1.2 Mathematical Patterns

1.2 Mathematical
Patterns
Warm-up
Page 11 #13
How are expressions written and graphed for arithmetic patterns?
Introduction to Arithmetic Sequences
How are expressions written and graphed for arithmetic patterns?
Definition of a Sequence
A sequence is an ordered list of numbers.
 Each number in the list is called a term of the
sequence.
 Infinite sequence has an infinite number of
terms.





First term is u1
Nth term is un
Term before is un-1
Graph of sequence is a scatterplot of ordered
pairs (term #, terms from set)
How are expressions written and graphed for arithmetic patterns?
Example

Find the next two terms in the sequence. Graph
the sequence.
2,5,8,...
Practice Page 19 #1
How are expressions written and graphed for arithmetic patterns?
Recursively Defined Sequence

First term is given and there is a method of
determining the nth term by using the terms that
precede it.
1 1

 Example:  , ,1, 2, 4,...
4 2

1
u1 
4
un  2  un1 for n  2
How are expressions written and graphed for arithmetic patterns?
Calculator Tips
Select Mode
 Arrow down to “Func Par Pol Seq”
 Arrow over to Seq and select enter
to make it dark.

1 u  2u
u1 
n
n 1 for n  2
4
1 1

 , ,1, 2, 4,...
4 2

How are expressions written and graphed for arithmetic patterns?
Application Example 1

A basketball is dropped from a height of 8 feet.
It hits the floor and bounces to a height of 6 feet.
It continues to bounce, and on each rebound it
rises to ¾ the height of the previous bounce.

Write a recursive formula for this problem.

Find the height of the ball on the fifth bounce.
How are expressions written and graphed for arithmetic patterns?
Application Example 2

Rick owns an automobile dealership. Last year,
he spent $16,000 on advertising. He plans to
increase his advertising expenditures by $1200
this year and in each subsequent year.

What will be the amount he spends on advertising in
the sixth year?
How are expressions written and graphed for arithmetic patterns?
Application Example 3

Ms. Long creates an endowment fund for her
alma mater. She places $250,000 in the fund to
start, and will add $50,000 to the fund each year.
She states that 25% of the total amount shall be
used each year for scholarships. How much will
be in the fund at the end of the sixth year?
How are expressions written and graphed for arithmetic patterns?
Practice:
Pages 19-20 #9,13,17
Homework:
Pages 19-20 #2-20 even
Ticket out the door…
What
is a recursive formula?