1. 6.3 Geometric Series (get a calculator)
Ms. Q
Riverdale high
1/23/2017

2. Definition of Geometric Sequence
6.3 Geometric Series
A sequence is geometric if the ratios of consecutive terms are the same.
2, 8, 32, 128, 512, . . .
geometric sequence
The common ratio, r, is 4.
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Definition of Geometric Sequence

3. The nth Term of a Geometric Sequence
6.3 Geometric Series
The nth term of a geometric sequence has the form
an = a1rn - 1
where r is the common ratio of consecutive terms of the sequence.
a1 = 15
15, 75, 375, , . . .
a2 = 15(5)
a3 = 15(52)
a4 = 15(53)
The nth term is 15(5n-1).
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The nth Term of a Geometric Sequence

4. Example: Finding the nth Term
6.3 Geometric Series
Example: Find the 9th term of the geometric sequence
7, 21, 63, . . .
a1 = 7
an = a1rn – 1 = 7(3)n – 1
a9 = 7(3)9 – 1 = 7(3)8
= 7(6561) = 45,927
The 9th term is 45,927.
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Example: Finding the nth Term

5. Definition of Summation Notation
6.3 Geometric Series
The sum of the first n terms of a sequence is represented by summation notation.
upper limit of summation
lower limit of summation
index of summation
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Definition of Summation Notation

6. Read the work example and answer question 4a&b as group (10 minutes).
6.3 Geometric Series
Textbook page489
Read the work example and answer question 4a&b as group (10 minutes).
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7. Answer question 5 as group (7 minutes).
6.3 Geometric Series
Textbook page490
Answer question 5 as group (7 minutes).
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8. Textbook page492, question 4. Group 1&2&7—a Group 3&4&8—b
6.3 Geometric Series
Textbook page492, question 4.
Group 1&2&7—a
Group 3&4&8—b
Group 5&6&9—c
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9. Page 493. Read the content in the bottom block. (5 minutes)
6.3 Geometric Series
Page 493. Read the content in the bottom block. (5 minutes)
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10. Work on page 494, question 8 as group.(5 minutes) 1&3&5—a 2&4&6—b
7&8&9&10—c
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11. Work on question 9 as group.(10 minutes)
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12. Work on problem 3, question 1 as group.
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13. Homework Page 497, question 2.
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