Unit 1 - Sequences & Functions Flashcards
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How is rate of change different from constant multiplier
Rate of change means you are adding the same number repeatedly to generate terms; constant multiplier means you are multiplying the same number repeatedly to generate terms
How do you check if a sequence is arithmetic?
Subtract pairs of consecutive terms. Do you get the same number each time? If yes –> seq is arithmetic
What is the sentence template for describing a sequence?
“The starting term is ____, then each following term is ____ than the previous term”
What are other names for a constant multiplier?
Growth factor & common ratio
How do you check if a sequence is geometric?
Divide pairs of consecutive terms. Is the ratio always the same? If yes –> seq is geometric
How, in general, do you describe a sequence?
By stating the starting term, then by saying how each term relates to the one before it
What is the next term in the sequence 3, 5, 7, 9, 11?
13 (add 2 each time)
How is a term related to a sequence?
Terms are the components of a sequence (if there aren’t any terms you can’t have a sequence)
What is the difference between arithmetic and geometric sequences?
Arithmetic sequences have a constant additive pattern, while geometric sequences have a constant multiplicative pattern
How do you find the constant multiplier if it isn’t obvious right away?
Divide pairs of consecutive terms
How do you find the rate of change if it isn’t obvious right away?
Subtract pairs of consecutive terms
Give an example of a sequence that is both arithmetic & geometric
2, 2, 2, 2, …
3, 3, 3, 3, …
1/2, 1/2, 1/2, …
(rate of change is 0 & constant multiplier is 1)
What is a sequence?
A list of numbers
What are the two main types of sequences we’ve studied?
Arithmetic & Geometric
What is a geometric sequence?
A sequience where each term is generated by multiplying a constant by the previous term
How do you know when your rate of change will be negative?
When the sequence is decreasing
What must be true about the constant multiplier, if the terms in a geometric sequence are increasing?
The constant multiplier is greater than 1
What is the constant in an arithmetic sequence called?
Common difference or rate of change
What equation is used for geometric sequences?
Current Term =
Constant * Previous Term
What equation is used for arithmetic sequences?
Current Term =
Constant + Previous Term
If a geometric sequence is decreasing, is the common ratio still called a growth factor?
Yes
What is the first number of a sequence called?
The “initial term” or “first term”
How can you tell when a geometric sequence is decreasing?
When the growth factor is a number less than 1
What are the 3 parts of the recursive function definition of a sequence?
- The starting term
- Rule for making new terms
- Domain of the rule
How can you identify whether a sequence is arithmetic or geometric from the function notation?
Look at the signs used (+constant for arithmetic; Xconstant for geometric)
What do we really mean by “the domain of the rule”?
It describes which terms the repetitive pattern is used for
What is the input of a sequence?
The term number / step number
What is the output of a sequence?
The value of the term
What information does f(n) give us?
The term number we are on AND the value of the term
ex: f(12)=50 tells us we are on term 12 and the value of that term is 50
What does f(n-1) represent?
The value of the previous term
What would the +5 in f(n)=f(n-1)+5 represent?
The rate of change is 5
How do you find the rate of change from a graph?
Look at your y-values and find the pattern by finding the difference in consecutive coordinate points.
What does a domain of “n≥2” really mean?
The rule gets used to find term 2 and every term after
What are the 4 ways we can represent sequences?
- List of numbers
- Table
- Graph
- Function
True or False:
Arithmetic & Geometric sequences always have recursive definitions
True
What are “consecutive” terms?
Terms next to each other in a sequence (aka terms that follow right after each other)
Why do we have to state the starting term in our recursive definition?
Because two sequences can have the same rule (ex: +2) but have different starting terms
How do you find the input of a sequence from a graph?
Look at the x-coordinates
How would you interpret f(1)=4?
Term #1 has a value of 4.
What is the recursive definition for the sequence: 2, 4, 6, 8, 10, 12, 14… ?
F(1) = 2,
F(n) = F(n - 1) + 2
for n ≥ 2
What is the advantage of using a graph over a table for sequences?
The graph can quickly show whether a sequence is arithmetic (looks linear) or geometric (looks exponential)
How is what n represents different from what f(n) represents?
n represents an input
f(n) represents an output
