3-6
3-6 Arithmetic
ArithmeticSequences
Sequences
Warm Up
Problem of the Day
Lesson Presentation
Course
Course
33
3-6 Arithmetic Sequences
Warm Up
Use the table to write an equation.
1. x
y
2.
3.
Course 3
1 2 3 4
5 10 15 20
x
1
2
y
–2.5
–5
x
y
1
5
2 3 4
8 11 14
y = 5x
3
4
–7.5 –10
y = –2.5x
y = 3x + 2
3-6 Arithmetic Sequences
Problem of the Day
A movie ticket at a certain theater costs
$4.50 for a child and $8.75 for an adult.
How much will it cost for a family of two
adults and three children to see a movie?
$31
Course 3
3-6 Arithmetic Sequences
Learn to identify and evaluate
arithmetic sequences.
Course 3
3-6 Arithmetic Sequences
Vocabulary
sequence
term
arithmetic sequence
common difference
Course 3
3-6 Arithmetic Sequences
A sequence is an ordered list of
numbers or objects, called terms. In
an arithmetic sequence, the
difference between one term and the
next is always the same. This
difference is called the common
difference. The common difference is
added to each term to get the next
term.
Course 3
3-6 Arithmetic Sequences
Additional Example 1: Finding the Common
Difference in an Arithmetic Sequence
Find the common difference in each arithmetic
sequence.
A. 11, 9, 7, 5, …
11, 9, 7, 5, …
The terms decrease by 2.
–2 –2 –2
The common difference is -2.
B. 2.5, 3.75, 5, 6.25, …
2.5, 3.75, 5, 6.25, … The terms increase by 1.25.
+1.25 +1.25 +1.25
The common difference is 1.25.
Course 3
3-6 Arithmetic Sequences
Check It Out: Example 1
Find the common difference in each arithmetic
sequence.
A. 2, 6, 10, 14, …
2, 6, 10, 14, …
The terms increase by 4.
+4 +4 +4
The common difference is 4.
B. 2.5, 5, 7.5, 10, …
2.5, 5, 7.5, 10, …
The terms increase by 2.5.
+2.5 +2.5 +2.5
The common difference is 2.5.
Course 3
3-6 Arithmetic Sequences
Additional Example 2: Finding Missing Terms in an
Arithmetic Sequence
Find the next three terms in the arithmetic
sequence –8, –3, 2, 7, ...
Each term is 5 more than the previous term.
7 + 5 = 12
12 + 5 = 17
17 + 5 = 22
Use the common difference to
find the next three terms.
The next three terms are 12, 17, and 22.
Course 3
3-6 Arithmetic Sequences
Check It Out: Example 2
Find the next three terms in the arithmetic
sequence –9, –6, –3, 0, ...
Each term is 3 more than the previous term.
0+3=3
3+3=6
6+3=9
Use the common difference to
find the next three terms.
The next three terms are 3, 6, and 9.
Course 3
3-6 Arithmetic Sequences
Additional Example 3A: Identifying Functions in
Arithmetic Sequences
Find a function that describes each arithmetic
sequence.
6, 12, 18, 24, …
n
1
2
3
4
n
Course 3
n•6
1
•
2
3
4
•
n
•
•
•
6
6
6
6
6
y
6
12
18
24
6n
Multiply n by 6.
y = 6n
3-6 Arithmetic Sequences
Additional Example 3B: Identifying Functions in
Arithmetic Sequences
Find a function that describes each arithmetic
sequence.
–4, –8, –12, –16, …
n
Course 3
1
2
3
y
n • (– 4)
–4
1 • (–4)
–8
2 • (–4)
3 • (–4) –12
4
n
4
n
•
•
(–4)
(–4)
–16
–4n
Multiply n by -4.
y = –4n
3-6 Arithmetic Sequences
Check It Out: Example 3A
Find a function that describes each arithmetic
sequence.
3, 6, 9, 12, …
n
1
2
3
4
n
Course 3
n•3
1
•
2
3
4
•
n
•
•
•
3
3
3
3
3
y
3
6
9
12
3n
Multiply n by 3.
y = 3n
3-6 Arithmetic Sequences
Check It Out: Example 3B
Find a function that describes each arithmetic
sequence.
–7, –14, –21, –28, …
n
1
2
3
4
n
Course 3
n • (-7)
y
1 • (-7) -7
2 • (-7) -14
3 • (-7) -21
4
n
•
•
(-7) -28
(-7) -7n
Multiply n by -7.
y = -7n
3-6 Arithmetic Sequences
Additional Example 4: Application
A DVD costs $3.95 to rent, plus $0.45 for
each day it is returned late. Find a function
that describes the arithmetic sequence, and
then find the total cost of renting the DVD
and returning it 9 days late.
n
1
2
3
4
n
Course 3
3.95 + 0.45n
3.95 + 0.45(1)
y
4.40
3.95 + 0.45(2)
3.95 + 0.45(3)
4.85
5.30
3.95 + 0.45(4)
5.75
3.95 + 0.45(5) 0.45n + 3.95
Multiply n by
$0.45, and
then add the
$3.95 rental
fee.
3-6 Arithmetic Sequences
Additional Example 4 Continued
A DVD costs $3.95 to rent, plus $0.45 for
each day it is returned late. Find a function
that describes the arithmetic sequence, and
then find the total cost of renting the DVD
and returning it 9 days late.
0.45n + 3.95
Write a function to find the 9th term.
0.45(9) + 3.95 Substitute 9 for n.
4.05 + 3.95
Multiply.
8.00
Add.
It will cost $8.00 to rent a movie and return it 9
days late.
Course 3
3-6 Arithmetic Sequences
Check It Out: Example 4
A personal pizza with cheese costs $3.99 to buy,
plus $0.25 for each additional topping. Find a
function that describes the arithmetic sequence,
and then find the total cost of buying a personal
pizza with 7 additional toppings.
n
1
2
3
4
n
Course 3
3.99 + 0.25n
3.99 + 0.25(1)
y
4.24
3.99 + 0.25(2)
3.99 + 0.25(3)
4.49
4.74
3.99 + 0.25(4)
4.99
3.99 + 0.25(5) 0.25n + 3.99
Multiply n by
$0.25, and
then add the
$3.99 pizza
cost.
3-6 Arithmetic Sequences
Check It Out: Example 4 Continued
A personal pizza with cheese costs $3.99 to buy,
plus $0.25 for each additional topping. Find a
function that describes the arithmetic sequence,
and then find the total cost of buying a personal
pizza with 7 additional toppings.
0.25n + 3.99
Write a function to find the 7th term.
0.25(7) + 3.99 Substitute 7 for n.
1.75 + 3.99
Multiply.
5.74
Add.
It will cost $5.74 to buy a personal pizza with 7
additional toppings.
Course 3
3-6 Arithmetic Sequences
Lesson Quiz: Part 1
Find the common difference in each arithmetic
sequence.
1. 4, 2, 0, –2, …
8 10
4
2. 3 , 2, 3 , 3 , …
–2
2
3
Find the next three terms in each arithmetic
sequence.
–2, –7, –12
3. 18, 13, 8, 3, …
4. 3.6, 5, 6.4, 7.8, …
Course 3
9.2, 10.6, 12
3-6 Arithmetic Sequences
Lesson Quiz: Part 2
Find a function that describes the arithmetic
sequence.
5. –5, –10, –15, –20, …
Possible Answer: y = –5n
6. –1, 2, 5, 8, …
Possible Answer: y = 3n – 4
7. A runner finishes a lap in 55 seconds. Her goal
is to decrease her time by two seconds every
week. Find a function that describes the arithmetic
sequence and find how many seconds her lap
should be after 12 weeks of training.
Possible Answer: s = -2w + 55; 31 seconds
Course 3