Geometric Sequences 9.3.notebook
May 26, 2016
Warm up
There is an arithmetic sequence in each column and row.
Fill in all the numbers.
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Geometric Sequences
The sequences in BLUE on the LEFT side are Geometric.
The sequences in RED on the RIGHT side are NOT Geometric. 3, 6, 12, 24, 48
1, 2, 3, 4
1, 2, 4, 8
6, 9, 12, 15, 18
18, ­6, 2, ­2/3
1, ­2 , 6, ­24
­3, 6, ­12, 24
1/2, 1/4, 1/6, 1/8
Write your own definition of a geometric sequence:
A geometric sequence is ...
The number that we _______________ is called the _____________________.
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Geometric Sequences 9.3.notebook
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Example 1: Determine whether each of the following is a geometric sequence. If it is, find the common ratio.
a. 6, 10, 14, 18, ...
b. 3, ­6, 12, ­24, 48, ...
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If the signs of the terms in a geometric series alternate (+, ­ +, ­, ...), then what can we say about the common ratio?
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Geometric Sequences 9.3.notebook
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New
Recall ...
recursive formula for arithmetic sequence
recursive formula for geometric sequence
explicit formula for arithmetic sequence
explicit formula for geometric sequence
Example 2: Write a rule for the terms in the geometric sequences below. Then, find the next term.
a. 3, 6, 12, 24, ...
b. 10, 2, 2/5, 2/25, ...
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Geometric Sequences 9.3.notebook
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Example 3: Finding the "middle terms"
a. Given that the 5th and 8th terms of a geometric sequence are 256 and 2048, respectively, write a rule for the nth term of the sequence.
b. Given a geometric sequence with a3 = 4 and a5 = 16, find all possibilities for a4.
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In Ex. 3 question b, why did we have multiple possibilities for the fourth term??!! In general, when would we have multiple possible values for the middle terms? Sep 14­10:10 PM
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Geometric Sequences 9.3.notebook
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Your turn...
a. Determine if the sequence is geometric, arithmetic, or neither.
b. If it is geometric, what is the common ratio?
c. If it is geometric, write an explicit formula for the sequence.
d. Then, find the 10th term in the sequence.
(If the sequence is not geometric, skip b­d)
8, 4, 2, 1, 0.5, ...
5, ­15, 30, ­25, 60, ...
1, ­4, 16, ­64, 256
0.001, 0.01, 0.1, 1, 10, ...
Using the recursive formula an = an ­ 1 2, find the next three terms if a1 = 3.
If a1 of a geometric sequence is 6, and a6 = 192, what are the values of a3 and a4 ? Explain your reasoning.
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Geometric Sequences 9.3.notebook
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Summary: Choose two!
1. What is a similarity between geometric sequences and arithmetic sequences? What are some differences?
2. Describe the difference between recursive and explicit formulas.
3. Describe how to calculate the missing terms in a geometric sequence.
Assignments: Geometric Sequences worksheet due next class; study for sequences quiz (next class)
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