6.3 geometric series
DESCRIPTION
6.3 Geometric Series. 3/25/2013. Geometric Sequence:. Is a sequence where each term is multiplied by the same factor in order to obtain the following term . Example:. 2, 8, 32, 128, 512, . . . . x 4 . x 4 . x 4 . x 4 . Common ratio (r):. 4 . Definition of Geometric Sequence. - PowerPoint PPT PresentationTRANSCRIPT
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6.3 Geometric Series
3/25/2013
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Geometric Sequence:
Is a sequence where each term is multiplied by the same factor in order to obtain the following term.
Example: 2, 8, 32, 128, 512, . . .
4
x 4 x 4 x 4
Common ratio (r):
x 4
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3
Rule of nth term of a geometric sequence
2, 8, 32, 128, 512, . . .
Common ratio, r = 4
1st term: 2nd term: 3rd term: 4th term: What’s the pattern?Rule:
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Geometric Series:
Expression formed by adding the terms of a geometric sequence.
Example(Finite): ∑
𝑛=0
8
6 (4 )𝑛
GeometricInfinite Series:
∑𝑛=0
∞
7( 12 )𝑛
6¿
7 ( 12 )0
+7 ( 12 )1
+7 ( 12 )2
+…. .
𝑎1r𝑎1
r
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a. Yesb. Each term is multiplied by 5.c. r = 5
a. Determine whether the following series is geometric.b. Explain why or why not.c. If it is geometric, find the common ratio.
a. Yesb. Each term is multiplied by .c. r = .
a. Nob. Each term is multiplied by different values.
a. Nob. Each term is multiplied by different values.
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Sum of the Finite Geometric Series
S = Sum of the series = first term in the series.
r = common ration = number of terms.
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Find the sum of the finite geometric series
+ +
r = 4n = since n started at 0 there are 9 terms
= 524,286
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Find the sum of the finite geometric series
r = n = 15
= 13.999957
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Sum of the Infinite Geometric Series
Only when common ratio is between 0 and 1.
S = Sum of the series
= first term in the series.r = common ratio
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Find the sum of the infinite geometric series
r = = 14
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Find the sum of the infinite geometric series
r = =
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Homework
WS 6.3 odd problems only
“I stayed up all night to see where the sun went. Then it dawned on me.”