AFM Ch.12 - Practice Test
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____
____
____
____
1. Form a sequence that has two arithmetic means between –13 and 89.
a. –13, 33, 43, 89
c. –18, –60, –102, –144
b. –18, –36, –72, –144
d. –18, –81, –144
2. Find the sum of the first 21 terms of the sequence 5, 9, 13, 17, 21, ...
a. 945
c. 947
b. 944
d. 946
3. Form a sequence that has two geometric means between –12 and –324.
a.
c. –12, –36, –108, –324
b.
d.
, 108,
4. Find the sum of the first 4 terms of the series.
a. –101
b. –103
c. –102
d. –104
____
5. Evaluate the limit, or state that the limit does not exist.
____
a. Limit does not exist
b.
1

5
6. Find the sum of the geometric series.
7
7
–
14 – 7
2
4
a.
b.
____
in expanded form and find the sum.
a.
b.
____
c.
d. 2002
28
3
7. Write
c.
d. 0
c.
d.
8. Find the seventh term of the expansion of
.
a.
c.
b.
d. none of these
Short Answer
9. Find the thirteenth term of an arithmetic sequence if the first term is 3 and the common difference is 3.
10. Find the sum of the first 17 terms of the arithmetic sequence 10, 14, 18, 22, 26...
11. Find the ninth term of the geometric sequence if a1 = 7 and r = 2.
12. Find the sum of the first 8 terms of the series.
13. Evaluate the limit, or state that the limit does not exist.
14. Find the sum of the series.
5
+ ...
20 + 10 + 5 +
2
15. Determine whether the series 20  100  500
is convergent or divergent.
16. Use the comparison test to determine whether the series is convergent or divergent.
1
1
1
49
64
81
17. Express the series
18. Find the 5th term of the expansion of
using sigma notation.
.
AFM Ch.12 - Practice Test
Answer Section
MULTIPLE CHOICE
1. ANS:
OBJ:
NAT:
TOP:
KEY:
2. ANS:
NAT:
KEY:
3. ANS:
OBJ:
NAT:
TOP:
KEY:
4. ANS:
NAT:
KEY:
5. ANS:
NAT:
KEY:
6. ANS:
NAT:
KEY:
7. ANS:
NAT:
KEY:
8. ANS:
NAT:
KEY:
A
PTS: 1
12-1.1 Find the nth term and arithmetic means of an arithmetic sequence.
NCTM AL.1
Find the nth term and arithmetic means of an arithmetic sequence.
nth Term | Arithmetic Means | Arithmetic Sequences
A
PTS: 1
OBJ: 12-1.2 Find the sum of n terms of an arithmetic series.
NCTM AL.1
TOP: Find the sum of n terms of an arithmetic series.
Arithmetic Series | Sum of Series
C
PTS: 1
12-2.1 Find the nth term and geometric means of a geometric sequence.
NCTM AL.1
Find the nth term and geometric means of a geometric sequence.
nth Term | Geometric Means | Geometric Sequences
C
PTS: 1
OBJ: 12-2.2 Find the sum of n terms of a geometric series.
NCTM AL.1
TOP: Find the sum of n terms of a geometric series.
Geometric Series | Sum of Series
B
PTS: 1
OBJ: 12-3.1 Find the limit of the terms of an infinite sequence.
NCTM AL.1
TOP: Find the limit of the terms of an infinite sequence.
Limits | Infinite Sequences
B
PTS: 1
OBJ: 12-3.2 Find the sum of an infinite geometric sequence.
NCTM AL.1
TOP: Find the sum of an infinite geometric sequence.
Geometric Sequences | Sum of Infinite Sequences
B
PTS: 1
OBJ: 12-5.1 Use sigma notation.
NCTM AL.1
TOP: Use sigma notation.
Sigma Notation
C
PTS: 1
OBJ: 12-6.1 Use the Binomial Theorem to expand binomials.
NCTM AL.1
TOP: Use the Binomial Theorem to expand binomials.
Binomial Theorem | Expand Binomials
SHORT ANSWER
9. ANS:
39
PTS:
NAT:
TOP:
KEY:
10. ANS:
714
1
OBJ: 12-1.1 Find the nth term and arithmetic means of an arithmetic sequence.
NCTM AL.1
Find the nth term and arithmetic means of an arithmetic sequence.
nth Term | Arithmetic Means | Arithmetic Sequences
PTS: 1
OBJ: 12-1.2 Find the sum of n terms of an arithmetic series.
NAT: NCTM AL.1
TOP: Find the sum of n terms of an arithmetic series.
KEY: Arithmetic Series | Sum of Series
11. ANS:
1792
PTS:
NAT:
TOP:
KEY:
12. ANS:
127.5
1
OBJ: 12-2.1 Find the nth term and geometric means of a geometric sequence.
NCTM AL.1
Find the nth term and geometric means of a geometric sequence.
nth Term | Geometric Means | Geometric Sequences
PTS: 1
OBJ: 12-2.2 Find the sum of n terms of a geometric series.
NAT: NCTM AL.1
TOP: Find the sum of n terms of a geometric series.
KEY: Geometric Series | Sum of Series
13. ANS:
6
PTS: 1
OBJ: 12-3.1 Find the limit of the terms of an infinite sequence.
NAT: NCTM AL.1
TOP: Find the limit of the terms of an infinite sequence.
KEY: Limits | Infinite Sequences
14. ANS:
40
PTS: 1
OBJ: 12-3.2 Find the sum of an infinite geometric sequence.
NAT: NCTM AL.1
TOP: Find the sum of an infinite geometric sequence.
KEY: Geometric Sequences | Sum of Infinite Sequences
15. ANS:
divergent
PTS: 1
OBJ: 12-4.1 Determine whether a series is convergent or divergent.
NAT: NCTM AL.1
TOP: Determine whether a series is convergent or divergent.
KEY: Convergent Series | Divergent Series
16. ANS:
convergent
PTS: 1
OBJ: 12-4.1 Determine whether a series is convergent or divergent.
NAT: NCTM AL.1
TOP: Determine whether a series is convergent or divergent.
KEY: Convergent Series | Divergent Series
17. ANS:
PTS: 1
OBJ: 12-5.1 Use sigma notation.
NAT: NCTM AL.1
TOP: Use sigma notation.
KEY: Sigma Notation
18. ANS:
PTS: 1
OBJ: 12-6.1 Use the Binomial Theorem to expand binomials.
NAT: NCTM AL.1
TOP: Use the Binomial Theorem to expand binomials.
KEY: Binomial Theorem | Expand Binomials