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Aim: Infinite Geometric Sequence/Series Course: Math Literacy
Do Now:
Aim: What are geometric sequences and series?
Find the sum of 12
1
4 0.3n
n
a1 = 4(0.3)1 = 1.2 n = 12r = 0.3
12
1 2 3 12
1
4 0.3 4 0.3 4 0.3 4 0.3 4 0.3n
n L
1
1
1
nrS a
r
121 0.31.2
1 0.3S
1.714
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Aim: Infinite Geometric Sequence/Series Course: Math Literacy
The Sum of a Infinite Geometric Sequence
Find the sum of 1
4 0.3n
n
a1 = 4(0.3)1 = 1.2 n = 12r = 0.3
1 2 3 12
1
4 0.3 4 0.3 4 0.3 4 0.3 4 0.3n
n
L
1
1
1
nrS a
r
1 0.31.2
1 0.3S
= ?
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Aim: Infinite Geometric Sequence/Series Course: Math Literacy
1
1
4(0.6)n
n
Find
= 4 + 4(0.6) + 4(0.6)2 + 4(0.6)3 + . .
The Sum of a Infinite Geometric Sequence
If |r| < 1, then the infinite geometric sequence a1, a1r2, a1r3, a1r4, . . . . a1rn - 1 . . . has the sum
11
1
n
nS a r
1
1
44(0.6) 10
1 0.6n
n
S
a1 = 4 and r = 0.6 - (|r| < 1)
1
1
a
r
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Aim: Infinite Geometric Sequence/Series Course: Math Literacy
Model Problem
Find the sum of 3 + 0.3 + 0.03 + 0.003 + . . .
r
araS n
n
1
11
11
1
1
aS
r
a1 = 3 and r = ?0.1
3 + 3(0.1) + 3(0.1)2 + 3(0.1)3 + . . .
3
1 (0.1)
3
0.9
13
3
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Aim: Infinite Geometric Sequence/Series Course: Math Literacy
Model Problems
Find the sum of the series.
160 + 80 + 40 + . . . , n = 6
Find the sum of the infinite series.
160 + 80 + 40 + . . . .
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Aim: Infinite Geometric Sequence/Series Course: Math Literacy
Model Problems
Find the sum of the geometric series.
2 3
3 1, , 5
8 4a a n
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Aim: Infinite Geometric Sequence/Series Course: Math Literacy
Model Problems
Express the series in sigma notation and find the sum.
54 + 18 + 6 + 2 + 2/3 + 2/9
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Aim: Infinite Geometric Sequence/Series Course: Math Literacy
Model Problems
Find a1.
Sn = -55, r = -2/3, n = 5
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Aim: Infinite Geometric Sequence/Series Course: Math Literacy
Model Problems
Find the nth term of the geometric sequence.
a2 = -18; a5 = 2/3; n = 6
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Aim: Infinite Geometric Sequence/Series Course: Math Literacy
Do Now:
Aim: What are geometric sequences?
Find the nth term of the geometric sequence.
a2 = -18; a5 = 2/3; n = 6