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©Evergreen Public Schools 2010
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• I can write an equation of a geometric sequence in explicit form.
What is explicit form for an arithmetic sequence?
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LaunchLaunchLaunchLaunchFrom section 8.1• What are the domains of the L(x)
and a(x) sequences?
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LaunchLaunchLaunchLaunch
Kingdom of Montarek
Day Plan 1 Day Plan 2 Day Plan 3
1 1 1 1 1 1
2 2 2 3 2 4
3 4 3 9 3 16
6 32 6 243 6 1024
10 512 10 19683 10 262144
63 4611686018427390000 15 4782969 11 1048576
64 9223372036854780000 16 14348907 12 4194304
From section 8.2• What are the domains of the plans?
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LaunchLaunchLaunchLaunchWhat do you think is true about the
domain of any sequence?
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SequencesSequences
a) 3, 6, 9, 12, 15, …b) 3, 6, 12, 24, 48, …1. What do the sequences have in
common?2. How are they different?3. Write an explicit rule with sequence
notation for each.
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Arithmetic SequencesArithmetic Sequences
L(x) = 2x + 1 and N(x) = 34 – 4x are arithmetic sequences.
They have a constant rate of change.
What is the rate of change of L(x) and N(x)?
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SequencesSequences
The sequences in the Kingdom of Montarek problems are geometric sequences.
They do not have a constant rate of change.
What is the rate of change of each plan?Plan 1: 1, 2, 4, 8, 16, …Plan 2: 1, 3, 9, 243, …Plan 3: 1, 4, 16, 1024, …
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Geometric SequencesGeometric Sequences
The sequences that are generated by repeated multiplication are called geometric sequences.
b) 3, 6, 12, 24, 48, … from slide 7 is an example.
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Geometric SequencesGeometric Sequences
b) 3, 6, 12, 24, 48, … from slide 7 is an example.
Look for a pattern in ratio of consecutive terms
Since the ratio is the same, we call it the common ratio.
6 12 ___ 48, , ,
3 6 12 ___
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Equations of Geometric Sequences
Equations of Geometric Sequences
We found the equations for the plans arePlan 1: Plan 2:
Plan 3:
b) What is the equation for 3, 6, 12, 24, …
12
2n
na 13
3n
na
14
4n
na
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Find next term and write equation with sequence
notation.
Find next term and write equation with sequence
notation.I1, -10, 100, -1000, …
II5, 10, 20, 40, …
III4, 12, 36, 108,
IV64, 16, 4, 1, …
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Find next term and write equation with sequence
notation.
Find next term and write equation with sequence
notation.I II
-243, -81, -27, -9, …
III IV4, 6, 9, 13.51 1 1
1, , , ,...2 4 8
1 1 1 1, , , ,...
2 4 8 16
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Write a formula to find the equations for geometric
sequences
Write a formula to find the equations for geometric
sequencesr = common ratio
In explicit forman =
n = term number
In recursive forman = and
an+1 = and
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Team PracticeTeam Practice
problem numbersan = 2 + 4(n – 1)
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DebriefDebrief
• Complete the sequence organizer for geometric sequences.
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5
3
12
4
Did you hit the target?• I can write an equation
of a geometric sequence in explicit form.
Rate your understanding of the target from 1 to 5.
5 is a bullseye!
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PracticePractice
Practice 8.3A Geometric Sequences problemsan = 1 + 4(n – 1)
