1. Module 1 Quiz Review

2. Linear Representation
Characteristics
Constant Rate of Change that is steady
A line
Usually 𝑦=𝑚𝑥+𝑏
Can also be written as
𝑓 𝑛 =𝑓 1 ±𝑑(𝑛−1)

3. Exponential Representation
Characteristics
Rate of Change is being multiplied/divided.
A rapidly increasing line. (think of a rocket shooting out)
Usually in the form 𝑦 =𝑎 𝑟 𝑥−1
Can be written as
𝑓 𝑛 =𝑓(1)∙ 𝑟 𝑛−1

4. Quadratic Representation
Characteristics
A quadratic sequence is a sequence of numbers in which the second difference between any two consecutive term is constant.
Ex: {1, 2, 4, 7, 11}
First difference is: 1, 2, 3, 4, …
Second difference is: 1, 1, 1, 1…
Usually has the form 𝑇 𝑛 =𝑎 𝑛 2 +𝑏𝑛+𝑐
To find the values of 𝑎, 𝑏, 𝑎𝑛𝑑 𝑐, we look at the first 3 terms in the sequence
𝑛=1 : 𝑇 1 =𝑎 𝑏 1 +𝑐=𝑎+𝑏+𝑐
𝑛=2 : 𝑇 2 =𝑎 𝑏 2 +𝑐=4𝑎+2𝑏+𝑐
𝑛=3 : 𝑇 3 =𝑎 𝑏 3 +𝑐=9𝑎+3𝑏+𝑐

5. Arithmetic vs. Geometric
Adding
Subtracting
Linear
Rate of change is constant
Graph is a line
Multiplying
Dividing
Exponential
Rate of change is a scale factor
Graph is a parabola
Equation
𝑓 𝑛 =𝑓 1 ±𝑑(𝑛−1)
𝑓 𝑛 =𝑓(1)∙ 𝑟 𝑛−1

6. So who has explicit or recursive?
BOTH arithmetic and geometric sequences can be written in EXPLICIT or RECURSIVE forms.
Explicit: does not contain f(n-1) or start with f(1)=____
Recursive: starts with f(1)=_____ and contains f(n)=f(n-1)