Name ___________________________________
Unit III-Part I: Relations and Functions
Learning Target #4: Arithmetic Sequences
A sequence is an ____________________________ of numbers that often form a
________________. Each number in the list is called a __________ of a sequence.
There are two types of sequences:
1. Arithmetic Sequence- a sequence that is formed by starting with an initial value
and _______________the same value repeatedly whether it is a positive number
or a negative number. (You ________ the same value repeatedly.)
2. Geometric Sequence- a sequence that is formed by starting with an initial value
and _______________ by the same value repeatedly whether it is a positive
number or a negative number. (You _____________ the same value repeatedly.)
Example 1: Describe the pattern in each sequence. What are the next two terms of
each sequence?
Test for Arithmetic: ________________________________________________
Test for Geometric: _________________________________________________
a) 5, 8, 11, 14, _____, _____
b) 2.5, 5, 10, 20, _____, ______
Test:
Test:
Description:
Description:
c) 5, 11, 17, 23, _____, _____
d) 400, 200, 100, 50, _____, ______
Test:
Test:
Description:
Description:
d) 2, -4, 8, -16, _____, _____
e) -15, -11, -7, -3, _____, ______
Test:
Test:
Description:
Description:
In an arithmetic sequence, the difference between the terms is constant. This
difference is called the ______________________________.
Example 2: Tell whether the sequence is arithmetic. If it is, what is the common
difference?
Sequence
a)
b)
c)
d)
Arithmetic? Yes or No
If yes, tell the
Common Difference (𝒅)
3, 8, 13, 18, …………
6, 9, 13, 17,………….
8, 15, 22, 30,……….
7, 9, 11, 13,……………
What if you wanted to find the 80th term of the arithmetic sequence? Would you want
to add the common difference 80 times?
Rule for an Arithmetic Sequence (Formula)
Writing an Explicit Formula
Example 3:
An online auction works as shown below. Write a rule to represent the bids as an
arithmetic sequence. What is the twelfth bid?
Example 4: A subway pass has a starting value of $100. After one ride, the value of the
pass is $98.25. After two rides, its value is $96.50. After three rides, its value is
$94.75.
a) Write a rule (formula) to represent the remaining value on the card as an
arithmetic sequence.
b) What is the value of the pass after 15 rides?
c) How many rides can be taken with the $100 pass?
Summary:
In your textbook, do page 278 #1-4 and #6-8
1. Description: ____________________________________________________
Next two terms are: _____ and _____
2. Description: ____________________________________________________
Next two terms are: _____ and _____
3. Yes or No
If yes, what is the common difference? _____
4. Yes or No
If yes, what is the common difference? _____
5. Don’t do this one
6. The common difference is ______ because _____________________________
______________________________________________________________
7. ______________________________________________________________
______________________________________________________________
______________________________________________________________
______________________________________________________________
8. ______________________________________________________________
______________________________________________________________
______________________________________________________________
______________________________________________________________