Free Printable Unit 2: Sequences, expressions an formulae

1.

The fifth term of a sequence is 23. The term-to-term rule is 'add 4'. Work out the first term of the sequence.

a)

7

b)

14

2.

Write down the first three terms of each sequence.

First term: -10

(term-to-term rule: 'add 20')

a)

-10, -30, -40

b)

-10, 10, 30

3.

25, 26, 27, 28, ..., ...

Work out the position-to-term for the sequence of numbers.

a)

Position number + 24

b)

Position number + 23

4.

Work out the first three terms and the 10th term of the sequences with the $n$ th term given.
$2n+4$

a)

1, 4, 7; 28

b)

6, 8, 10; 24

5.

The $n$ th term of a sequence is $2n-1$ . Work out the first three terms and the ninth term of the sequence.

a)

1, 3, 5; 17

b)

5, 7, 9; 18

6.

a. $3x-7$ when $x=-5$
b. $\frac{x}{4}-10\$ when $x=20$
c. $\frac{x}{2}+\frac{y}{10}$ when $x=30$ and $y=-30$

a)

a. $-22$
b. $-5$
c. $12$

b)

a. $-22$

b. $5$

c. $13$

7.

Work out the value of the expression:
a. $a^2-6$ when $a=4$
b. $5n^{3\ }$ when $n=-2$

a)

a. $10$
b. $-40$

b)

a. $10$
b. $-39$

8.

Find the n^th term of the following sequence...

5, 9, 13, 17...

a)

4n + 1

b)

n + 4

c)

4n -1

d)

n - 4

9.

Find the n^th term of the following sequence...

8, 13, 18, 23...

a)

5n + 3

b)

n + 5

c)

3n + 5

d)

n + 3

10.

Find the n^th term of the following sequence...

2, 5, 8, 11...

a)

3n - 1

b)

n + 3

c)

3n + 1

d)

n - 1

11.

Find the n^th term of the following sequence...

11, 17, 23, 29...

a)

6n + 5

b)

5n + 6

c)

6n - 5

d)

5n - 6

12.

Find the n^th term of the following sequence...

4, 7, 10, 13...

a)

3n - 1

b)

n + 3

c)

3n + 1

d)

n - 1

13.

Generate the first 4 terms of the sequence with the following n^th term rule...

4n - 1

a)

4, 3, 2, 1...

b)

5, 9, 13, 17...

c)

3, 7, 11, 15...

d)

4, 5, 6, 7...

14.

Generate the first 4 terms of the sequence with the following n^th term rule...

3n + 7

a)

10, 13, 16, 19...

b)

10, 14, 18, 22...

c)

7, 19, 13, 16...

d)

10, 17, 24, 31...

15.

Generate the first 4 terms of the sequence with the following n^th term rule...

5n - 2

a)

3, 8, 13, 18...

b)

3, 5, 7, 9...

c)

3, 1, -1, -3...

d)

3, 7, 11, 15...

16.

Generate the first 4 terms of the sequence with the following n^th term rule...

8n - 4

a)

4, 12, 20, 28...

b)

12, 20, 28, 36...

c)

4, 8, 12, 16...

d)

12, 16, 20, 24...

17.

What is the 20th term in the sequence...

9n - 4

a)

176

b)

108

c)

184

d)

180

18.

Given the nth term is 9-2n, what is the 7th term?

a)

1

b)

-4

c)

-5

d)

-3

19.

Given the nth term is 3n+1 what is the 10th term?

a)

29

b)

33

c)

40

d)

31

20.

The nth term of a sequence is: 4n - 1.

Is 35 a number in the sequence?

a)

Yes

b)

No

21.

The nth term of a sequence is 5n - 2.

Is 23 a number in the sequence?

a)

Yes

b)

No

22.

What is the term to term rule for this sequence?

3, 7, 11, 15, ...

a)

+6

b)

+5

c)

+4

d)

+2

23.

What is the term to term rule for this sequence?

97, 86, 75, 64, ...

a)

+8

b)

-11

c)

+11

d)

-8

24.

Find the next three terms in the arithmetic sequence: 25, 34, 43, 52, ...

a)

63, 72, 81...

b)

70, 79, 88...

c)

79, 88, 97...

d)

61, 70, 79...

25.

Find the 25th term if the sequence whose nth term is: 10n-51

a)

250

b)

199

c)

200

d)

159

26.

Find the nth term of...

8,13,18,23...

a)

5n + 3

b)

3n + 5

c)

5n - 2

d)

-2n + 5

27.

Find the function that describes the arithmetic sequence of 16, 17, 18, 19.....

a)

y = 16n

b)

y = n + 15

c)

y = 15 + 1

d)

y = 17n - 1

28.

Find the next three terms if the sequence

9, 109, 209, 309, 409, ....

a)

509, 559, 579

b)

410, 415, 420

c)

509, 609, 709

29.

Find the next three terms of the sequence

14, 34, 54, 74, 94, ....

a)

104, 108, 112

b)

95, 96, 97

c)

104, 114, 124

d)

114, 134, 154

30.

Work out this expression

j/4 when j = - 20

a)

-5

b)

-10

c)

5

31.

Work out this expression

8m - 5, when m = -2

a)

21

b)

-15

c)

-21

32.

Work out this expression

20 - 3n when n = 9

a)

-9

b)

-7

c)

-13

33.

Find 6h when h = -3!

a)

18

b)

-18

c)

12

34.

Find 2x + 3y when x = 4, and y = 5

a)

25

b)

24

c)

23

35.

x² + 5 when x = 4 is ...

a)

21

b)

23

c)

22

36.

m² - n² when m = 7 and n = 8 is ...

a)

-15

b)

-10

c)

15

37.

2d² + 1 when d = 5 is ...

a)

51

b)

50

c)

16

38.

y²/2 when y = 4 is ...

a)

8

b)

4

c)

6

39.

2y³ when y = 3 is ...

a)

27

b)

54

c)

18

Unit 2: Sequences, expressions an formulae

Total questions: 39

Worksheet time: 1hrs 18mins

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