9.3 geometric sequences and series
DESCRIPTION
9.3 Geometric Sequences and Series. Common Ratio. In the sequence 2, 10, 50, 250, 1250, ….. Find the common ratio. Rule of Geometric Sequences. Let a 1 = 2 r = 5 Find a 6. Rule of Geometric Sequences. Let a 2 = 12 a 3 = 36 Find a 6. Rule of Geometric Sequences. - PowerPoint PPT PresentationTRANSCRIPT
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9.3 Geometric Sequences and Series
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Common Ratio
In the sequence
2, 10, 50, 250, 1250, …..
Find the common ratio n
n
a
ar 1
5
510
50
550
250
r
r
r
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Rule of Geometric Sequences
Let a1 = 2
r = 5
Find a6
1
1
n
n raa
6250
52
6
16
6
a
a
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Rule of Geometric Sequences
Let a2 = 12
a3 = 36
Find a6
1
1
n
n raa
31236 r
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Rule of Geometric Sequences
Let a2 = 12
a3 = 36
r = 3
Find a6
1
1
n
n raa
1
1
2
1
13
13
4936
336
336
a
a
a
aa
9722434
34
6
16
6
a
a
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Finite Sum
The equation to find the Finite Sum of a Geometric Sequence
rr
araorSnn
k
k
n
11
11
1
1
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Finite Sum
Let a1 = 7, r = 3.
Find the sum of the first 9 terms
rr
araorSnn
k
k
n
11
11
1
1
2
1968317
31
31737
99
1
1
k
k
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Finite Sum
Let a1 = 7, r = 3.
Find the sum of the first 9 terms
rr
araorSnn
k
k
n
11
11
1
1
887,68984172
196827
2
1968317
31
31737
99
1
1
k
k
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How many terms
0.25 + 0.75 + 2.25 + …….. = 820
Common ratio
rr
arann
k
k
1
11
1
1
1
325.0
75.0
375.0
25.2
r
r
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How many terms
0.25 + 0.75 + 2.25 + …….. = 820
Common ratio 3
rr
arann
k
k
1
11
1
1
1
n
n
n
n
n
36561
316560
318
1820
2
31
4
1820
31
3125.0820
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How many terms
0.25 + 0.75 + 2.25 + …….. = 820
Common ratio 3
rr
arann
k
k
1
11
1
1
1
n
n
n
n
n
36561
316560
318
1820
2
31
4
1820
31
3125.0820
8
3log6561log
6561log
36561
3
n
n
n
n
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Infinite Geometric Series
If |r| < 1, it works
r
ara
n
n
11
1
1
1
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Infinite Geometric Series
Since |0.2| < 1, it works. Let a1 = 42
5.528.042
2.0142
2.0421
1
n
n
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Homework
Page 640 – 641
# 5, 15, 25, 35,
45, 55, 65, 75,
85, 105, 115
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Homework
Page 640 – 641
# 3, 9, 27, 81, 113