Sec 1 Maths Number sequences and patterns worksheet with answers

A free Sec 1 Maths worksheet on number sequences and patterns: 8 questions, 30 marks, short questions first and then structured ones, in the school exam style. The answers and full worked solutions are on the last page.

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Sec 1 Maths worksheet: Number sequences and patterns

Total: 30 marksSuggested time: 45 minutes

Name: ______________________________Class: ____________ Date: ____________

Answer all questions. Show all your working. Give non-exact answers correct to 3 significant figures, or 1 decimal place for angles in degrees, unless the question says otherwise.

Section A

Determine whether

69

is a term of the sequence

8, \ 11, \ 14, \ 17, \ \ldots

Answer[2]

(a)Find the missing term in the sequence

10, \ 17, \ 24, \ \_\_\_, \ 38

Answer (a)[1]

(b)Find the missing term in the sequence

7, \ 15, \ \_\_\_, \ 31, \ 39

Answer (b)[1]

The diagram shows Figures 3, 4 and 5 of a pattern made with matchsticks. Find the number of matchsticks needed for Figure 6.

Answer[3]

(a)Find the missing term in the sequence

9, \ 7, \ \_\_\_, \ 3, \ 1

Answer (a)[1]

(b)Write down the next term of the sequence

7, \ 14, \ 23, \ 34, \ \ldots

Answer (b)[3]

Section B

(a)Determine whether

-91

is a term of the sequence

49, \ 45, \ 41, \ 37, \ \ldots

Answer (a)[2]

(b)(i)Write down the next term of the sequence

16, \ 8, \ 0, \ -8, \ \ldots

Answer (b)(i)[1]

(b)(ii)Write down the next term of the sequence

5, \ -10, \ 20, \ -40, \ \ldots

Answer (b)(ii)[1]

(a)Determine whether

-49

is a term of the sequence

10, \ 8, \ 6, \ 4, \ \ldots

Answer (a)[2]

(b)The diagram shows Figures 1, 2 and 3 of a pattern made with matchsticks. Find an expression, in terms of

n

, for the number of matchsticks in Figure

n

Answer (b)[3]

(a)(i)Write down the next term of the sequence

18, \ 23, \ 28, \ 33, \ \ldots

Answer (a)(i)[1]

(a)(ii)Find the missing term in the sequence

7, \ 15, \ \_\_\_, \ 31, \ 39

Answer (a)(ii)[1]

(b)The diagram shows Figures 3, 4 and 5 of a pattern made with matchsticks. Find the number of matchsticks needed for Figure 6.

Answer (b)[3]

(a)(i)Find the missing term in the sequence

10, \ 17, \ 24, \ \_\_\_, \ 38

Answer (a)(i)[1]

(a)(ii)Find the missing term in the sequence

20, \ \_\_\_, \ 26, \ 29, \ 32

Answer (a)(ii)[1]

(b)The diagram shows Figures 2, 3 and 4 of a pattern made with matchsticks. Find the number of matchsticks needed for Figure 20.

Answer (b)[3]

END OF PAPER

Answers and worked solutions

Question 1

Answer: NO[2]

\mathstrut 11 - 8 =

3

\mathstrut 8 - 3 =

5

3n + 5 = 69

n = \dfrac{64}{3}

n

is not a whole number, so

69

is not a term: No.

Question 2

(a)Answer:

\mathstrut 24 + 7 =

31

[1]

\mathstrut 17 - 10 =

7

\mathstrut 24 + 7 =

31

(b)Answer:

\mathstrut 15 + 8 =

23

[1]

\mathstrut 15 - 7 =

8

\mathstrut 15 + 8 =

23

Question 3

Answer:

\mathstrut 11 + 1 \times 2 =

13

[3]

\text{Figure 3:}

7

\text{Figure 4:}

9

\text{Figure 5:}

11

\mathstrut 9 - 7 =

2

Figure

3, 4, 5

: matchsticks

7, 9, 11

, going up by

2

each time.

\mathstrut 11 + 1 \times 2 =

13

Question 4

(a)Answer:

\mathstrut 7 + (-2) =

5

[1]

\mathstrut 7 - 9 =

-2

\mathstrut 7 + (-2) =

5

(b)Answer:

\mathstrut 34 + 13 =

47

[3]

\mathstrut 14 - 7 =

7

\mathstrut 23 - 14 =

9

\mathstrut 34 - 23 =

11

\mathstrut 9 - 7 =

2

\mathstrut 11 + 2 =

13

\mathstrut 34 + 13 =

47

Question 5

(a)Answer: YES[2]

\mathstrut 45 - 49 =

-4

\mathstrut 49 - (-4) =

53

53 - 4n = -91

n = 36

n

is a whole number, so

-91

is the 36th term: Yes.

(b)(i)Answer:

\mathstrut -8 + (-8) =

-16

[1]

\mathstrut 8 - 16 =

-8

\mathstrut -8 + (-8) =

-16

(b)(ii)Answer:

\mathstrut (-40) \times (-2) =

80

[1]

The differences are not equal: each term is the one before it multiplied by the same number.

\mathstrut (-10) \div 5 =

-2

\mathstrut (-40) \times (-2) =

80

Question 6

(a)Answer: NO[2]

\mathstrut 8 - 10 =

-2

\mathstrut 10 - (-2) =

12

12 - 2n = -49

n = \dfrac{61}{2}

n

is not a whole number, so

-49

is not a term: No.

(b)Answer:

2n + 1

matchsticks[3]

\text{Figure 1:}

3

\text{Figure 2:}

5

\text{Figure 3:}

7

\mathstrut 5 - 3 =

2

Figure

1, 2, 3

: matchsticks

3, 5, 7

, going up by

2

each time.

\mathstrut 3 - 2 =

1

2n + 1

matchsticks

Question 7

(a)(i)Answer:

\mathstrut 33 + 5 =

38

[1]

\mathstrut 23 - 18 =

5

\mathstrut 33 + 5 =

38

(a)(ii)Answer:

\mathstrut 15 + 8 =

23

[1]

\mathstrut 15 - 7 =

8

\mathstrut 15 + 8 =

23

(b)Answer:

\mathstrut 16 + 1 \times 3 =

19

[3]

\text{Figure 3:}

10

\text{Figure 4:}

13

\text{Figure 5:}

16

\mathstrut 13 - 10 =

3

Figure

3, 4, 5

: matchsticks

10, 13, 16

, going up by

3

each time.

\mathstrut 16 + 1 \times 3 =

19

Question 8

(a)(i)Answer:

\mathstrut 24 + 7 =

31

[1]

\mathstrut 17 - 10 =

7

\mathstrut 24 + 7 =

31

(a)(ii)Answer:

\mathstrut 20 + 3 =

23

[1]

\mathstrut 29 - 26 =

3

\mathstrut 20 + 3 =

23

(b)Answer:

\mathstrut 5 \times 20 + 1 =

101

[3]

\text{Figure 2:}

11

\text{Figure 3:}

16

\text{Figure 4:}

21

\mathstrut 16 - 11 =

5

Figure

2, 3, 4

: matchsticks

11, 16, 21

, going up by

5

each time.

5n + 1

, since Figures

2, 3, 4

have

11, 16, 21

matchsticks

\mathstrut 5 \times 20 + 1 =

101

Practice questions by skill

Sec 1 Maths Number sequences and patterns worksheet with answers

In the print window, choose Save as PDF to download it.

Need the formulas first? Read the Number sequences and patterns notes. Or practise it online with step-by-step help when you get one wrong.

Section B

(a)Determine whether

-91

is a term of the sequence

49, \ 45, \ 41, \ 37, \ \ldots

Answer (a)[2]

(b)(i)Write down the next term of the sequence

16, \ 8, \ 0, \ -8, \ \ldots

Answer (b)(i)[1]

(b)(ii)Write down the next term of the sequence

5, \ -10, \ 20, \ -40, \ \ldots

Answer (b)(ii)[1]

Answers and worked solutions

Question 1

Answer: NO[2]

\mathstrut 11 - 8 =

3

\mathstrut 8 - 3 =

5

3n + 5 = 69

n = \dfrac{64}{3}

n

is not a whole number, so

69

is not a term: No.

Question 2

(a)Answer:

\mathstrut 24 + 7 =

31

[1]

\mathstrut 17 - 10 =

7

\mathstrut 24 + 7 =

31

(b)Answer:

\mathstrut 15 + 8 =

23

[1]

\mathstrut 15 - 7 =

8

\mathstrut 15 + 8 =

23

Question 3

Answer:

\mathstrut 11 + 1 \times 2 =

13

[3]

\text{Figure 3:}

7

\text{Figure 4:}

9

\text{Figure 5:}

11

\mathstrut 9 - 7 =

2

Figure

3, 4, 5

: matchsticks

7, 9, 11

, going up by

2

each time.

\mathstrut 11 + 1 \times 2 =

13

Question 4

(a)Answer:

\mathstrut 7 + (-2) =

5

[1]

\mathstrut 7 - 9 =

-2

\mathstrut 7 + (-2) =

5

(b)Answer:

\mathstrut 34 + 13 =

47

[3]

\mathstrut 14 - 7 =

7

\mathstrut 23 - 14 =

9

\mathstrut 34 - 23 =

11

\mathstrut 9 - 7 =

2

\mathstrut 11 + 2 =

13

\mathstrut 34 + 13 =

47

Question 5

(a)Answer: YES[2]

\mathstrut 45 - 49 =

-4

\mathstrut 49 - (-4) =

53

53 - 4n = -91

n = 36

n

is a whole number, so

-91

is the 36th term: Yes.

(b)(i)Answer:

\mathstrut -8 + (-8) =

-16

[1]

\mathstrut 8 - 16 =

-8

\mathstrut -8 + (-8) =

-16

(b)(ii)Answer:

\mathstrut (-40) \times (-2) =

80

[1]

The differences are not equal: each term is the one before it multiplied by the same number.

\mathstrut (-10) \div 5 =

-2

\mathstrut (-40) \times (-2) =

80

Question 6

(a)Answer: NO[2]

\mathstrut 8 - 10 =

-2

\mathstrut 10 - (-2) =

12

12 - 2n = -49

n = \dfrac{61}{2}

n

is not a whole number, so

-49

is not a term: No.

(b)Answer:

2n + 1

matchsticks[3]

\text{Figure 1:}

3

\text{Figure 2:}

5

\text{Figure 3:}

7

\mathstrut 5 - 3 =

2

Figure

1, 2, 3

: matchsticks

3, 5, 7

, going up by

2

each time.

\mathstrut 3 - 2 =

1

2n + 1

matchsticks

Question 7

(a)(i)Answer:

\mathstrut 33 + 5 =

38

[1]

\mathstrut 23 - 18 =

5

\mathstrut 33 + 5 =

38

(a)(ii)Answer:

\mathstrut 15 + 8 =

23

[1]

\mathstrut 15 - 7 =

8

\mathstrut 15 + 8 =

23

(b)Answer:

\mathstrut 16 + 1 \times 3 =

19

[3]

\text{Figure 3:}

10

\text{Figure 4:}

13

\text{Figure 5:}

16

\mathstrut 13 - 10 =

3

Figure

3, 4, 5

: matchsticks

10, 13, 16

, going up by

3

each time.

\mathstrut 16 + 1 \times 3 =

19

Question 8

(a)(i)Answer:

\mathstrut 24 + 7 =

31

[1]

\mathstrut 17 - 10 =

7

\mathstrut 24 + 7 =

31

(a)(ii)Answer:

\mathstrut 20 + 3 =

23

[1]

\mathstrut 29 - 26 =

3

\mathstrut 20 + 3 =

23

(b)Answer:

\mathstrut 5 \times 20 + 1 =

101

[3]

\text{Figure 2:}

11

\text{Figure 3:}

16

\text{Figure 4:}

21

\mathstrut 16 - 11 =

5

Figure

2, 3, 4

: matchsticks

11, 16, 21

, going up by

5

each time.

5n + 1

, since Figures

2, 3, 4

have

11, 16, 21

matchsticks

\mathstrut 5 \times 20 + 1 =

101