8.1
Defining and Using Sequences and Series
8.2
Analyzing Arithmetic Sequences and Series
8.3
Analyzing Geometric Sequences and Series
8.4
Finding Sums of Infinite Geometric Series
8.5
Using Recursive Rules with Sequences
8
Sequences and Series
Marching Band
(p. 423)
Skydiving
(p. 431)
Tree Farm
(p. 449)
Fish Population
(p. 445)
Museum Skylight
(p. 416)
Ma
rc
hi
ng
B
an
d
(p
.
423)
Mu
seum
Skyligh
t
(p 416)
(
)
Tree Farm
(p
.
449)
Fi h P
l ti
(
445)
SEE the Big Idea
Chapter Learning Target:
Understand sequences and series.
Chapter Success Criteria:
■
I can define and use sequences and series.
■
I can describe how to find sums of infinite
geometric series.
■
I can analyze arithmetic and geometric
sequences and series.
■
I can explain how to write recursive rules
for sequences.
407
Maintaining Mathematical Proficiency
Evaluating Functions
Example 1
Evaluate the function
y
=
2
x
2
−
10 for the values
x
=
0, 1, 2, 3, and 4.
Input,
x
2
x
2
−
10
Output,
y
0
2(
0
)
2
−
10
−
10
1
2(
1
)
2
−
10
−
8
2
2(
2
)
2
−
10
−
2
3
2(
3
)
2
−
10
8
4
2(
4
)
2
−
10
22
Copy and complete the table to evaluate the function.
1.
y
=
3
−
2
x
2.
y
=
5
x
2
+
1
3.
y
=
−
4
x
+
24
x
y
1
2
3
x
y
2
3
4
x
y
5
10
15
Solving Equations
Example 2
Solve the equation 45
=
5(3)
x
.
45
=
5(3)
x
Write original equation.
45
—
5
=
5(3)
x
—
5
Divide each side by 5.
9
=
3
x
Simplify.
log
3
9
=
log
3
3
x
Take log
3
of each side.
2
=
x
Simplify.
Solve the equation. Check your solution(s).
4.
7
x
+
3
=
31
5.
1
—
16
=
4
(
1
—
2
)
x
6.
216
=
3(
x
+
6)
7.
2
x
+
16
=
144
8.
1
—
4
x
−
8
=
17
9.
8
(
3
—
4
)
x
=
27
—
8
10.
ABSTRACT REASONING
The graph of the exponential decay function
f
(
x
)
=
b
x
has an
asymptote
y
=
0. How is the graph of
f
different from a scatter plot consisting of the points
(1,
b
1
), (2,
b
1
+
b
2
), (3,
b
1
+
b
2
+
b
3
), . . .? How is the graph of
f
similar?
Dynamic Solutions available at
BigIdeasMath.com
408
Chapter 8
Sequences and Series
Mathematical
Practices
Using Appropriate Tools Strategically
Mathematically proficient students consider the available tools when
solving a mathematical problem.
Monitoring Progress
Use a spreadsheet to help you answer the question.
1.
A pilot flies a plane at a speed of 500 miles per hour for 4 hours. Find the total distance
flown at 30-minute intervals. Describe the pattern.
2.
A population of 60 rabbits increases by 25% each year for 8 years. Find the population at
the end of each year. Describe the type of growth.
3.
An endangered population has 500 members. The population declines by 10% each decade
for 80 years. Find the population at the end of each decade. Describe the type of decline.
4.
The top eight runners finishing a race receive cash prizes. First place receives $200, second
place receives $175, third place receives $150, and so on. Find the fifth through eighth place
prizes. Describe the type of decline.
Using a Spreadsheet
You deposit $1000 in stocks that earn 15% interest compounded annually. Use a spreadsheet to
find the balance at the end of each year for 8 years. Describe the type of growth.
