Math Lesson­2.notebook
March 27, 2015
Daily Objective
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Students will learn how to tell if a sequence is geometric by examining the ratio of consecutive terms of a sequence.
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Math Lesson­2.notebook
March 27, 2015
12.3 Geometric Sequences
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geometric sequence: the pattern of the sequence is a common ratio
common ratio: the constant ratio of any term to the previous term; denoted by r
Ex. 1: Tell whether the sequence is geometric.
a. 4, 10, 18, 28, 40,...
b. 625, 125, 25, 5, 1,...
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Math Lesson­2.notebook
March 27, 2015
WB 12.3 p.175
1. 3, 5, 7, 9, 11,...
2. 5, 10, 20, 40, 80,...
3. 100, 50, 25, 25/2, 25/4,...
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Math Lesson­2.notebook
March 27, 2015
Rule for a Geometric Sequence
The nth term of a geometric sequence with first term a1 and common ratio r is given by:
an = a1(r)n­1
Ex. 2: Write a rule for the nth term of the sequence.
Then find a7.
b. 152, ­76, 38, ­19,...
a. 4, 20, 100, 500,...
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Math Lesson­2.notebook
March 27, 2015
Ex. 3: One term of a geometric sequence is a4 = 12. The common ratio is r = 2.
a. Write a rule for the nth term.
b. Graph the sequence.
y
x
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Math Lesson­2.notebook
March 27, 2015
WB 12.3 p.175
7. r = 3, a1 = 2
8. r = 1/10, a2 = 4
9. r = ­1/2, a3 = 8
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Math Lesson­2.notebook
March 27, 2015
Ex. 4: Two terms of the sequence are a3 = ­48 and a6 = 3072. Find a rule for the nth term.
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Math Lesson­2.notebook
March 27, 2015
WB 12.3 p.175
10. a1 = 1, a3 = 9
11. a3 = 24, a5 = 96
12. a2 = 2, a6 = 512
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Math Lesson­2.notebook
March 27, 2015
12.3 WB Today!
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