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 = , t1 is:

A 1

B

C 3

D 2

E 3

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


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 , , , ..., S12 is equal to:

A

B 6

C 78

D 39

E 12

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 For the sequence 12, 6, 3, ..., S8 is equal to:

A 23

B 23

C

D

E 23


12 For the sequence 12, -6, 3, ..., S¥ is equal to:

A

B 0

C 24

D 8

E ¥

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 $22774.56

D $28254.91

E $48919.24

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 the 6th term.

2 For the arithmetic sequence –18, -14, -10, ..., find:

a the first term, a, and the common difference, d

b the 26th term.

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.

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 Find the total number of hours she spends training during the first 15weeks.

3 In which week will the time Billie spends training first exceed 50 hours?

Answers to Chapter 5 Practice Test

Answers to multiple-choice questions

1 C

2 C

3 C

4 C

5 B

6 B

7 D

8 D

9 B

10 E

11 B

12 D

13 C

14 B

15 A

Answers to short-answer (technology-free) questions

1 a 19

b 91

2 a a = -18, d = 4

b 82

3 56

4 a 165

b 465

5 30

6 9

7

8

Answers to extended-response questions

1 390

2 b 381.27

3 16th

© Evans, Avery, Wallace, Lipson 2006 1