Geometric Sequences

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Geometric Sequences
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Geometric Sequences

• A sequence which has a constant ratio between
  terms. The rule is exponential.
• Example 4, 8, 16, 32, 64,
• (generator is x2)

n t(n)
1 4
2 8
3 16
4 32
5 64
x2
Discrete
x2
x2
0 1 2 3 4 5 6
x2
3
Working Backwards for a Rule
First find the generator and the n0 term. Then
write the equation Ex
0
1 2 3 4
3, 15, 75, 375,
x5
Sequences start with n1 now!
t(0) is not in the sequence! Do not include it in
tables or graphs!
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Positive Multipliers

• In a geometric sequence, if the multiplier is
• Less than one but greater than 0 (0ltblt1)
• Equal to 1 (b1)
• Greater than 1 (bgt1)

The sequence decreases.
The sequence is constant.
The sequence increases.
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Example of a Sequence

• 2, 6, 18, 54, ___, ___,
• Generator
• Representations
• Table Rule

162
486
Multiply by 3
n t(n)
1 2
2 6
3 18
4 54
5 162
6 486
n t(n)
1
2
3
4
5
6
t(n) 2/3(3)n
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Example of a Sequence

• 625, 125, 25, 5, ___, ___,
• Generator
• Representations
• Table Rule

1
0.2
Multiply by 1/5 (0.2)
n t(n)
1 625
2 125
3 25
4 5
5 1
6 0.2
n t(n)
1
2
3
4
5
6
t(n) 3125(0.2)n
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Sequences v Functions

• Sequence t(n)
• Function f(x)

Positive Integers (sometimes 0)
Domain (n)
Can be all Real numbers
Range (t(n))
Discrete
The Graph is
Can be all Real numbers
Domain (x)
Can be all Real numbers
Range (f(x))
can be Continuous
The Graph