Unit 1 - Sequences & Functions

Question 1

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How is rate of change different from constant multiplier

Answer 1

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

Question 2

How do you check if a sequence is arithmetic?

Answer 2

Subtract pairs of consecutive terms. Do you get the same number each time? If yes –> seq is arithmetic

Question 3

What is the sentence template for describing a sequence?

Answer 3

“The starting term is ____, then each following term is ____ than the previous term”

Question 4

What are other names for a constant multiplier?

Answer 4

Growth factor & common ratio

Question 5

How do you check if a sequence is geometric?

Answer 5

Divide pairs of consecutive terms. Is the ratio always the same? If yes –> seq is geometric

Question 6

How, in general, do you describe a sequence?

Answer 6

By stating the starting term, then by saying how each term relates to the one before it

Question 7

What is the next term in the sequence 3, 5, 7, 9, 11?

Answer 7

13 (add 2 each time)

Question 8

How is a term related to a sequence?

Answer 8

Terms are the components of a sequence (if there aren’t any terms you can’t have a sequence)

Question 9

What is the difference between arithmetic and geometric sequences?

Answer 9

Arithmetic sequences have a constant additive pattern, while geometric sequences have a constant multiplicative pattern

Question 10

How do you find the constant multiplier if it isn’t obvious right away?

Answer 10

Divide pairs of consecutive terms

Question 11

How do you find the rate of change if it isn’t obvious right away?

Answer 11

Subtract pairs of consecutive terms

Question 12

Give an example of a sequence that is both arithmetic & geometric

Answer 12

2, 2, 2, 2, …
3, 3, 3, 3, …
1/2, 1/2, 1/2, …

(rate of change is 0 & constant multiplier is 1)

Question 13

What is a sequence?

Answer 13

A list of numbers

Question 14

What are the two main types of sequences we’ve studied?

Answer 14

Arithmetic & Geometric

Question 15

What is a geometric sequence?

Answer 15

A sequience where each term is generated by multiplying a constant by the previous term

Question 16

How do you know when your rate of change will be negative?

Answer 16

When the sequence is decreasing

Question 17

What must be true about the constant multiplier, if the terms in a geometric sequence are increasing?

Answer 17

The constant multiplier is greater than 1

Question 18

What is the constant in an arithmetic sequence called?

Answer 18

Common difference or rate of change

Question 19

What equation is used for geometric sequences?

Answer 19

Current Term =
Constant * Previous Term

Question 20

What equation is used for arithmetic sequences?

Answer 20

Current Term =
Constant + Previous Term

Question 21

If a geometric sequence is decreasing, is the common ratio still called a growth factor?

Answer 21

Yes

Question 22

What is the first number of a sequence called?

Answer 22

The “initial term” or “first term”

Question 23

How can you tell when a geometric sequence is decreasing?

Answer 23

When the growth factor is a number less than 1

Question 24

What are the 3 parts of the recursive function definition of a sequence?

Answer 24

1. The starting term
2. Rule for making new terms
3. Domain of the rule

Question 25

How can you identify whether a sequence is arithmetic or geometric from the function notation?

Answer 25

Look at the signs used (+constant for arithmetic; Xconstant for geometric)

Question 26

What do we really mean by “the domain of the rule”?

Answer 26

It describes which terms the repetitive pattern is used for

Question 27

What is the input of a sequence?

Answer 27

The term number / step number

Question 28

What is the output of a sequence?

Answer 28

The value of the term

Question 29

What information does f(n) give us?

Answer 29

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

Question 30

What does f(n-1) represent?

Answer 30

The value of the previous term

Question 31

What would the +5 in f(n)=f(n-1)+5 represent?

Answer 31

The rate of change is 5

Question 32

How do you find the rate of change from a graph?

Answer 32

Look at your y-values and find the pattern by finding the difference in consecutive coordinate points.

Question 33

What does a domain of “n≥2” really mean?

Answer 33

The rule gets used to find term 2 and every term after

Question 34

What are the 4 ways we can represent sequences?

Answer 34

1. List of numbers
2. Table
3. Graph
4. Function

Question 35

True or False:

Arithmetic & Geometric sequences always have recursive definitions

Answer 35

True

Question 36

What are “consecutive” terms?

Answer 36

Terms next to each other in a sequence (aka terms that follow right after each other)

Question 37

Why do we have to state the starting term in our recursive definition?

Answer 37

Because two sequences can have the same rule (ex: +2) but have different starting terms

Question 38

How do you find the input of a sequence from a graph?

Answer 38

Look at the x-coordinates

Question 39

How would you interpret f(1)=4?

Answer 39

Term #1 has a value of 4.

Question 40

What is the recursive definition for the sequence: 2, 4, 6, 8, 10, 12, 14… ?

Answer 40

F(1) = 2,
F(n) = F(n - 1) + 2
for n ≥ 2

Question 41

What is the advantage of using a graph over a table for sequences?

Answer 41

The graph can quickly show whether a sequence is arithmetic (looks linear) or geometric (looks exponential)

Question 42

How is what n represents different from what f(n) represents?

Answer 42

n represents an input
f(n) represents an output