Math I Period 1

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Warm-Up Evaluating Functions
Evaluate the following
1. f(4)
13
20
2. f(-3)
104
3. f(-9)
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CCGPS Alg2/19/2013
UNIT QUESTION How do we graph functions, and
what can be done to change the way they
look? Todays Question How do we write the
function to represent a sequence?
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CCGPS Alg2/19/2013
(I.N. p49) MCC9-12.F.IF.3 Recognize that
sequences are functions, sometimes defined
recursively, whose domain is a subset of the
integers
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Sequences

• Everyday a radio station asks a question for a
  prize of 150. If the fifth caller does not
  answer correctly, the prize money increased by
  150 each day until someone correctly answers
  their question.
• Make a list of the prize money for a week from
  Monday to Friday if no one gets it right.

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Contest

• Monday 150
• Tuesday 300
• Wednesday 450
• Thursday 600
• Friday 750

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Sequences

• These prize amounts form a sequence.
• Sequence A function whose domain is a set of
  consecutive natural numbers.
• What would be the value on Day 6? Day 7?

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Sequences

• The values in the range are called the terms of
  the sequence.
• Domain 1 2 3 4....n
• Range a1 a2 a3 a4.. an
• A sequence can be specified by an equation or
  rule.

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Contest

• a1 150

a2 300
a3 450
a4 600
a5 750
an represents a general term where n can be any
number. What is the closed formula for an?
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Sequences

• Sequences can continue forever. We can calculate
  as many terms as we want as long as we know the
  rule or equation for an.
• Example
• 2, 8, 14, 20, ___ , ___,. _____ .

an 6n - 4
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Writing Terms of a Sequence
an 2n 3 Find a1, a2, a3, a4, a5
a1 -1 First Term a2 1 Second Term a3
3 Third Term a4 5 Fourth Term a5 7 Fifth
Term
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Practice
an -5n 20 Find a1, a2, a3, a4, a5
a1 First Term a2 Second Term a3 Third
Term a4 Fourth Term a5 Fifth Term
15 10 5 0 -5
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Arithmetic Sequences
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Writing Rules Using the Formulaan a1 d(n-1)
a1 3 First Term a2 5 Second Term a3
7 Third Term a4 9 Fourth Term an nth Term
What is the rule? an ???
an 3 2(n-1)
an 3 2n 2 2n 1
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Writing Rules for a Sequence
a1 2 First Term a2 6 Second Term a3
10 Third Term a4 14 Fourth Term an nth Term
What is the rule? an ???
an 4n - 2
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Writing Rules for a Sequence
a1 7 First Term a2 4 Second Term a3
1 Third Term a4 -2 Fourth Term an ?? nth
Term
What is the rule? an ???
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Try This!
a1 5 First Term a2 12 Second Term a3
19 Third Term a4 26 Fourth Term an nth Term
What is the rule? an ???
an 7n - 2
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EOCT Practice

• 77 b) 81
• c) 84 d) 86

b
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EOCT Practice
Find the 25th term of the sequence 7, 11, 15, 19,
23, ...

• 103 b) 104
• c) 107 d) 111

a
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Homework

• Practice Sequence Worksheet