Chapter 5 Sequences and series: Practice Test
Multiple-choice questions
1
The first three terms of the sequence defined by the rule tn = 3n + 1 are
A
1, 2, 3
B
1, 4, 7
C
4, 7, 10
D
3, 6, 9
E
2, 5, 8
2
If t1 = 10, tn + 1 = tn  3, then t5 is
A
7
B
5
C
2
D
8
E
1
3
For the sequence defined by the difference equation tn = 2 (n2 + n) + 2, t1 is
1
A
1
B
1
2
C
D
3
2
E
32
1
4
The 70th term of the arithmetic sequence –12, –8,  4, … is
A
74
B
260
C
264
D
268
E
228
5
If 308 is the nth term of the sequence 3, 8, 13, …, then n is equal to
A
61
B
62
C
63
D
5
E
3
6
Hamish keeps track of the number of hits on his website over the month of
April. He gets 32 hits on the 1st of April, 36 on the 2nd of April, 40 on the 3rd of
April, and so on, every day for the month of April. The number of hits he has on
15th of April is
A
84
B
88
C
15
D
92
E
900
© Evans, Avery, Wallace, Lipson 2006
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Chapter 5 Sequences and series: Practice Test
7
Hamish keeps track of the number of hits on his website over the month of
April. He gets 32 hits on the 1st of April, 36 on the 2nd of April, 40 on the 3rd of
April, and so on, every day for the month of April. The total number of hits he
has for the month of April is
A
900
B
148
C
30
D
2700
E
2852
8
Given the arithmetic sequence 2 , 2, 2 , ..., S12 is equal to
2
A
11 2
2
B
C
D
E
6 2
78 2
39 2
12 2
3 2
9
Given the arithmetic sequence 20, 16, 12, ..., S11 is equal to
A
400
B
0
C
20
D
400
E
20
10
The 10th term of the sequence 12, 6, 3, … is
A
B
C
D
E
11
3
32
1
32
9
128
1
128
3
128
For the sequence 12, 6, 3, ..., S8 is equal to
3
A
23 32
B
23 32
29
D
3
8
3
32
E
23 16
C
3
© Evans, Avery, Wallace, Lipson 2006
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Chapter 5 Sequences and series: Practice Test
12
For the sequence 12, 6, 3, ..., S is equal to
A
1
2
B
C
D
E
0
24
8

13
On its first day of business a pie stall sells 40 pies. Each day the number of pies
sold increases by 12.5%. After 1 week, the number of pies the stall will have
sold, to the nearest whole number, is
A
81
B
91
C
410
D
501
E
329
14
$4000 is invested at 6.5% p.a. compounded annually. The value of the
investment after 5 years is
A
$5145.87
B
$5480.35
C
$22 774.56
D
$28 254.91
E
$48 919.24
15
$4000 is invested at 6.5% p.a. compounded annually. The value of the
investment will first exceed $7000 after
A
9 years
B
10 years
C
11 years
D
8 years
E
2 years
Short-answer questions (technology-free)
1
For the sequence defined by the difference equation tn = 3(n2  n) + 1, find
a
the 3rd term
b
2
the 6th term.
For the arithmetic sequence –18, 14, 10, ..., find
a
the first term, a, and the common difference, d
b
the 26th term.
© Evans, Avery, Wallace, Lipson 2006
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Chapter 5 Sequences and series: Practice Test
3
For an arithmetic sequence, the 2nd term is 16 and the 10th term is 16. Find
the 20th term.
4
a
Find the sum of the first 10 multiples of 3.
b
Find the sum of the next 10 multiples of 3.
5
Find the 6th term of the sequence 4, 6, 9, ...
6
36, 31, 26 are the first three terms of a sequence. Find n if the nth term is 4.
7
Evaluate the series 16  8 + 4  2 + ...
8
The first term of a geometric sequence is 8 and the sum to infinity is 32. Find r.
© Evans, Avery, Wallace, Lipson 2006
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Chapter 5 Sequences and series: Practice Test
Extended-response questions
Ashley and Billie are swimmers training for a competition.
1 Ashley trains for 12 hours in the first week. She decides to increase the amount
of time she spends training by 2 hours per week. Find the total number of
hours she spends training during the first 15 weeks.
2
Billie also trains for 12 hours in the first week. She decides to train for 10%
longer each week than the previous week.
a
Show that in the third week she trained for 1452 hours.
b
3
Find the total number of hours she spends training during the first
15 weeks.
In which week will the time Billie spends training first exceed 50 hours?
© Evans, Avery, Wallace, Lipson 2006
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Chapter 5 Sequences and series: Practice Test
Answers to Chapter 5 Practice Test
Answers to multiple-choice questions
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
C
C
C
C
B
B
D
D
B
E
B
D
C
B
A
Answers to short-answer (technology-free) questions
1
2
3
4
a
b
a
b
56
a
b
19
91
a = 18, d = 4
82
165
465
3
5
30 8
6
9
7
8
32
3
3
4
Answers to extended-response questions
1
2
3
390
b
381.27
16th
© Evans, Avery, Wallace, Lipson 2006
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