Specific Sequences

1
Specific Sequences

• Arithmetic Sequence A sequence which has a
  constant difference between terms.
• 1, 4, 7, 10, 13,
• (generator is 3)
• Geometric Sequence A sequence which has a
  constant ratio between terms.
• 4, 8, 16, 32, 64,
• (generator is x2)

2
Sequences v Functions

• Sequence t(n)
• Function f(n)

Domain Positive Integers (sometimes 0)
Domain
Domain Can be all Real numbers
Domain
3
Percent Increase

• What is a 15 increase of 100?
• First Step
• Second Step

.
15.
0.15
.
.
What about Percent Decrease?
1
2
Multiplier
4
pPod Problem
Week Sales
0
1
2
3
4
n
100
100.1.150
115
100.1.15
100.1.151
132.25
100.1.15.1.15
100.1.152
152.09
100.1.15.1.15.1.15
100.1.153
174.9
100.1.15.1.15.1.15.1.15
100.1.154
100.1.15n
5
Exponential Growth

• A P ( 1 r ) t
• A Amount after time t
• P Principle (starting amount)
• t Time after starting point
• r Decimal increase ( 100)

What about Exponential Decay?
Learning Log
6
Exponential Decay

• A(t) P ( 1 r ) t
• A(t) Amount as a function in terms of t
• P Principle (starting amount)
• t Time after starting point
• r Decimal decrease ( 100)

Learning Log