CHAPTER
ADDITIONAL RESOURCES
• Chapter 11 Resource Book
Chapter Test (3 levels) (p. 81)
SAT/ACT Chapter Test (p. 87)
Alternative Assessment (p. 88)
•
Test and Practice Generator
11
Chapter Standardized Test
TEST-TAKING STRATEGY If the answers to a question are formulas, substitute the given
numbers into the formulas to test the possible answers.
1. MULTIPLE CHOICE What is the next term in the
sequence 1, 4, 9, 16, 25, . . .? C
A
¡
D
¡
B
¡
E
¡
34
38
C
¡
35
36
39
2. MULTIPLE CHOICE Which series is represented by
4
∑ (4i º 2)? A
A 2 + 6 + 10 + 14
¡
B º2 + 2 + 6 + 10
¡
C 4 + 8 + 12 + 16
¡
D 6 + 10 + 14 + 18
¡
E 2 + 6 + 10 + 14 + . . .
¡
i=1
Qu. Standard
Qu. Standard
Finite geometric series
Infinite arithmetic series
None of these
5
E
C
¡
240
243
5. MULTIPLE CHOICE What is a rule for the nth term
of the arithmetic sequence with a14 = 9 and common
difference d = 2? E
B
¡
D
¡
an = 2n + 7
an = 2n º 9
an = 2n + 11
an = 2n º 15
an = 2n º 19
terms of the series 2 + 17 + 32 + 47 + . . . ? C
696
696
1600
18,800
B
¡
E
¡
an = º4(3)n º 1
C
¡
E
¡
an = ºᎏᎏ(3)n º 1
3
4
D
¡
an = ºᎏᎏ(3)n º 1
1
3
an = 4(3)n º 1
i
≈ 13.30
C
¡
≈ 13.32
≈ 29.97
9. MULTIPLE CHOICE What is the sum of the series
‡
∑ 5(1.2)i º 1? E
i=1
A º30
B
¡
¡
D 30
E
¡
¡
º25
C
¡
25
The series has no sum.
A
¡
3
ᎏᎏ
10
B
¡
3
ᎏᎏ
8
D
¡
38 3
ᎏᎏ
1 00 0
E
¡
38
ᎏᎏ
99
C
¡
38
ᎏᎏ
100
11. MULTIPLE CHOICE What is a recursive rule for the
sequence 2, 6, 18, 54, . . .? D
A
¡
B
¡
C
¡
D
¡
E
¡
an = 2(3)n º 1
an = 3(2)n º 1
a1 = 2, an = an º 1 + 4
a1 = 2, an = 3an º 1
a1 = 3, an = 2an º 1
12. MULTIPLE CHOICE What is the fourth term of the
6. MULTIPLE CHOICE What is the sum of the first 50
A
¡
D
¡
B
¡
the repeating decimal 0.3838 . . .? E
4. MULTIPLE CHOICE What is the sum of the series
A
¡
C
¡
E
¡
4
3
10. MULTIPLE CHOICE Which fraction is equivalent to
Infinite geometric series
131
an = ºᎏᎏ(3)n º 1
9
Finite arithmetic series
B
¡
E
¡
A
¡
∑ 20冉ᎏ12ᎏ冊 ? D
i=0
A ≈ 11.74
B
¡
¡
D ≈ 39.96
E
¡
¡
32 + 16 + 8 + 4 + 2 + 1? B
∑ (n3 + 3)?
n=0
A 128
¡
D 242
¡
of the geometric sequence with a3 = º12 and
common ratio r = 3? A
8. MULTIPLE CHOICE What is the sum of the series
3. MULTIPLE CHOICE What type of series is
A
¡
B
¡
C
¡
D
¡
E
¡
7. MULTIPLE CHOICE What is a rule for the nth term
18,235
C
¡
18,475
19,125
Chapter 11 Sequences and Series
sequence defined by the recursive rule
a1 = 3, an = n + an º 1 º 7? C
A
¡
D
¡
º1
º10
B
¡
E
¡
º6
º11
C
¡
º9
QUANTITATIVE COMPARISON In Exercises 13 and 14, choose the statement
that is true about the given quantities.
A
¡
B
¡
C
¡
D
¡
The quantity in column A is greater.
The quantity in column B is greater.
The two quantities are equal.
The relationship cannot be determined from the given information.
Column A
Column B
10
The tenth term of the sequence
defined by an = 7 º 2n
13.
∑ (7 º 2n)
A
nn when n is an integer greater than 1
B
15d.
n=1
n! when n is an integer greater than 1
14.
15c.
n 1
an 1
MULTI-STEP PROBLEM Use the pattern of checkerboard quilts at the right.
15.
b. What does an represent in each quilt? The number of blue squares.
n2
1
e. Use the rule an = ᎏᎏ + ᎏᎏ[1 º (º1)n] to find an for n = 1, 2, 3, 4, 5, 6, 7, 8.
2
4
a = 1, 2, 5, 8, 13, 18, 25, 32
i=1
7
16d. ∑ (3i + 4)
i=0
11
n=2
a2 = 2
16e. ∑ (3i – 8)
i=4
n
Compare with the results in your table. What can you conclude about the
sequence defined by this rule? they are the same; neither arithmetic or geometric
16. MULTI-STEP PROBLEM Use the series 4 + 7 + 10 + 13 + 16 + 19 + 22 + 25.
8(4 + 25)
a. Use a formula to find the sum of the series. Show your work. }} = 116
2
b. Find the sum of the series without using a formula. Explain your method.
16f. Sample answer: All answers
have a sum of 8 terms, so the
indices of summation are 7 apart.
Each has a 3i term. The actual
indices vary, as does the constant term.
17c. Sample answer: the points follow an exponential curve with a
y-intercept of 200, y decreasing
as x increases, becoming
asymptotic to the x-axis as
x · ∞.
n=3
a3 = 5
Multiply the sum of the first and last terms by 4; 116
c. Write the series with summation notation. Use 1 as the lower limit of
n=4
a4 = 8
summation. See margin.
d. Write the series with summation notation. Use 0 as the lower limit of
summation. See margin.
e. Write the series with summation notation. Use 4 as the lower limit of
y
100
summation. See margin.
f.
4 5 6 7 8
8 13 18 25 32
16c. ∑ (3i + 1)
c. Draw the next four quilts in the pattern. See margin.
d. Complete a table that gives n and an for n = 1, 2, 3, 4, 5, 6, 7, 8. See margin.
3
5
8
n=1
a1 = 1
a. What does n represent in each quilt? The number of squares on a side.
2
2
Writing Compare your answers to parts (c), (d), and (e). Describe any
similarities and differences. Which of these ways do you prefer to write the
series? Explain your answer. See margin.
75
50
17. MULTI-STEP PROBLEM Use the sequence 100, 50, 25, 12.5, . . . .
25
a. Is this sequence arithmetic, geometric, or neither? Is it finite or infinite? geometric; infinite
0
0
1
2
3
4
5
6
7
8 x
b. Write the next three terms of the sequence. 6.25, 3.125, 1.5625
c. Graph the sequence. Describe the curve on which the points lie. See margin.
1 nº1
d. Write an explicit rule for the nth term of the sequence. 100 }2}
1
e. Write a recursive rule for the sequence. a1 = 100; an = }2} an º 1
冉冊
冉冊
f. Find the twelfth term of the sequence. Which rule from parts (d) and (e) did
you use? Explain your choice. }25}; Sample answer: I used the explicit rule from part (d) since it is the fastest way
512
to find the answer.
Chapter Standardized Test
697
697