Lesson 5-10
Pages 249-252
Arithmetic and
Geometric Sequences
Lesson Check 5-9
What you will learn!
1. How to find the terms of
arithmetic sequences.
2. How to find the terms of
geometric sequences.
Sequence
Arithmetic sequence
Term
Common difference
Geometric sequence
Common ratio
What you really need to know!
A sequence is
an ordered list
of numbers.
What you really need to know!
An arithmetic sequence is a
sequence in which the difference
between any two consecutive
terms, called the common
difference, is the same. In the
sequence 2, 9, 16, 23, 30, . . . ,
the common difference is 7.
What you really need to know!
A geometric sequence is a
sequence in which the quotient
of any two consecutive terms,
called the common ratio, is the
same. In the sequence 1, 4, 16,
64, 256, . . , the common ratio is
4.
Example 1:
State whether the sequence
-5, -1, 3, 7, 11, …
is arithmetic. If it is, state the
common difference and write
the next three terms.
Example 2:
-5, -1, 3, 7, 11, 15, 19, 23
Subtract
Common difference
11 – 7
7–3
3 – -1
-1 – -5
4
4
4
4
Arithmetic! + 4
Example 2:
State whether the sequence
0, 2, 6, 12, 20, …
is arithmetic. If it is, state the
common difference and write
the next three terms.
Example 2:
0, 2, 6, 12, 20 …
Subtract
Common difference
20 – 12
12 – 6
6–2
2–0
8
6
4
2
Not Arithmetic!
Example 3:
State whether the sequence
2, 4, 4, 8, 8, 16, 16 …
is geometric. If it is, state the
common ratio and write the
next three terms.
Example 3:
2, 4, 4, 8, 8, 16, 16, …
Divide
Common ratio
16 ÷ 16
16 ÷ 8
8÷8
8÷4
4÷4
4÷2
1
2
1
2
1
2
Not Geometric!
Example 4:
State whether the sequence
27, -9, 3, -1, 1/3, …
is geometric. If it is, state the
common ratio and write the
next three terms.
Example 4:
27, -9, 3, -1, 1/3, -1/9, 1/27, -1/81
Divide
Common ratio
1/3 ÷ -1 -1/3
-1 ÷ 3
-1/3
3 ÷ -9
-1/3
-9 ÷ 27
-1/3
Geometric! • -1/3
Page 251
Guided Practice
#’s 3-9
Read:
Pages 249-250
with someone at
home and study
examples!
Homework: Pages 251-252
#’s 10-28 even,
32, 33, 36-49
Lesson Check Ch-5
Page
736
Lesson 5-10
Lesson Check Ch-5
Study Guide and Review
Pages
254-258
#’s 1-81
(Odd answers in back of book)
Prepare for Test!
Page
259
#’s 1-33
Lesson Check Ch-5
Prepare for Test!
Pages
260-261
#’s 1-22