Sec 1 G2 Maths Number sequences and patterns worksheet with answers

A free Sec 1 G2 Maths worksheet on number sequences and patterns: 6 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 G2 Maths worksheet: Number sequences and patterns

Total: 30 marksSuggested time: 50 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

Find an expression, in terms of

n

, for the

n

th term of the sequence

52, \ 47, \ 42, \ 37, \ \ldots

Answer[2]

The diagram shows Figures 3, 4 and 5 of a pattern made with matchsticks. Find an expression, in terms of

n

, for the number of matchsticks in Figure

n

Answer[3]

(a)Find the missing term in the sequence

-3, \ 0, \ 3, \ \_\_\_, \ 9

Answer (a)[1]

(b)Write down the next term of the sequence

17, \ 26, \ 37, \ 50, \ \ldots

Answer (b)[3]

Section B

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

-3, \ 0, \ 3, \ \_\_\_, \ 9

Answer (a)(i)[1]

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

-2, \ 6, \ -18, \ 54, \ \ldots

Answer (a)(ii)[1]

(b)Determine whether

139

is a term of the sequence

13, \ 19, \ 25, \ 31, \ \ldots

Answer (b)[2]

(c)The diagram shows Figures 1, 2 and 3 of a pattern made with matchsticks. Find the number of matchsticks needed for Figure 20.

Answer (c)[3]

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

29, \ 35, \ 41, \ 47, \ \ldots

Answer (a)(i)[1]

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

21, \ 30, \ \_\_\_, \ 48, \ 57

Answer (a)(ii)[1]

(b)Find an expression, in terms of

n

, for the

n

th term of the sequence

11, \ 18, \ 25, \ 32, \ \ldots

Answer (b)[2]

(c)The diagram shows Figures 2, 3 and 4 of a pattern made with matchsticks. Find the number of matchsticks needed for Figure 100.

Answer (c)[3]

(a)The diagram shows Figures 1, 2 and 3 of a pattern made with matchsticks. Find the number of matchsticks needed for Figure 4.

Answer (a)[3]

(b)(i)Find an expression, in terms of

n

, for the

n

th term of the sequence

7, \ 11, \ 15, \ 19, \ \ldots

Answer (b)(i)[2]

(b)(ii)Determine whether

165

is a term of the sequence

13, \ 21, \ 29, \ 37, \ \ldots

Answer (b)(ii)[2]

END OF PAPER

Answers and worked solutions

Question 1

Answer:

T_n = 57 - 5n

[2]

\mathstrut 47 - 52 =

-5

\mathstrut 52 - (-5) =

57

T_n = 57 - 5n

Question 2

Answer:

5n + 1

matchsticks[3]

\text{Figure 3:}

16

\text{Figure 4:}

21

\text{Figure 5:}

26

\mathstrut 21 - 16 =

5

Figure

3, 4, 5

: matchsticks

16, 21, 26

, going up by

5

each time.

\mathstrut 16 - 3 \times 5 =

1

5n + 1

matchsticks

Question 3

(a)Answer:

\mathstrut 3 + 3 =

6

[1]

\mathstrut 0 - (-3) =

3

\mathstrut 3 + 3 =

6

(b)Answer:

\mathstrut 50 + 15 =

65

[3]

\mathstrut 26 - 17 =

9

\mathstrut 37 - 26 =

11

\mathstrut 50 - 37 =

13

\mathstrut 11 - 9 =

2

\mathstrut 13 + 2 =

15

\mathstrut 50 + 15 =

65

Question 4

(a)(i)Answer:

\mathstrut 3 + 3 =

6

[1]

\mathstrut 0 - (-3) =

3

\mathstrut 3 + 3 =

6

(a)(ii)Answer:

\mathstrut 54 \times (-3) =

-162

[1]

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

\mathstrut 6 \div (-2) =

-3

\mathstrut 54 \times (-3) =

-162

(b)Answer: YES[2]

\mathstrut 19 - 13 =

6

\mathstrut 13 - 6 =

7

6n + 7 = 139

n = 22

n

is a whole number, so

139

is the 22nd term: Yes.

(c)Answer:

\mathstrut 5 \times 20 + 1 =

101

[3]

\text{Figure 1:}

6

\text{Figure 2:}

11

\text{Figure 3:}

16

\mathstrut 11 - 6 =

5

Figure

1, 2, 3

: matchsticks

6, 11, 16

, going up by

5

each time.

5n + 1

, since Figures

1, 2, 3

have

6, 11, 16

matchsticks

\mathstrut 5 \times 20 + 1 =

101

Question 5

(a)(i)Answer:

\mathstrut 47 + 6 =

53

[1]

\mathstrut 35 - 29 =

6

\mathstrut 47 + 6 =

53

(a)(ii)Answer:

\mathstrut 30 + 9 =

39

[1]

\mathstrut 30 - 21 =

9

\mathstrut 30 + 9 =

39

(b)Answer:

T_n = 7n + 4

[2]

\mathstrut 18 - 11 =

7

\mathstrut 11 - 7 =

4

T_n = 7n + 4

(c)Answer:

\mathstrut 5 \times 100 + 2 =

502

[3]

\text{Figure 2:}

12

\text{Figure 3:}

17

\text{Figure 4:}

22

\mathstrut 17 - 12 =

5

Figure

2, 3, 4

: matchsticks

12, 17, 22

, going up by

5

each time.

5n + 2

, since Figures

2, 3, 4

have

12, 17, 22

matchsticks

\mathstrut 5 \times 100 + 2 =

502

Question 6

(a)Answer:

\mathstrut 16 + 1 \times 5 =

21

[3]

\text{Figure 1:}

6

\text{Figure 2:}

11

\text{Figure 3:}

16

\mathstrut 11 - 6 =

5

Figure

1, 2, 3

: matchsticks

6, 11, 16

, going up by

5

each time.

\mathstrut 16 + 1 \times 5 =

21

(b)(i)Answer:

T_n = 4n + 3

[2]

\mathstrut 11 - 7 =

4

\mathstrut 7 - 4 =

3

T_n = 4n + 3

(b)(ii)Answer: YES[2]

\mathstrut 21 - 13 =

8

\mathstrut 13 - 8 =

5

8n + 5 = 165

n = 20

n

is a whole number, so

165

is the 20th term: Yes.

Sec 1 G2 Maths Number sequences and patterns worksheet with answers

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

Or practise it online with step-by-step help when you get one wrong.

Section B

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

-3, \ 0, \ 3, \ \_\_\_, \ 9

Answer (a)(i)[1]

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

-2, \ 6, \ -18, \ 54, \ \ldots

Answer (a)(ii)[1]

(b)Determine whether

139

is a term of the sequence

13, \ 19, \ 25, \ 31, \ \ldots

Answer (b)[2]

(c)The diagram shows Figures 1, 2 and 3 of a pattern made with matchsticks. Find the number of matchsticks needed for Figure 20.

Answer (c)[3]

Answers and worked solutions

Question 1

Answer:

T_n = 57 - 5n

[2]

\mathstrut 47 - 52 =

-5

\mathstrut 52 - (-5) =

57

T_n = 57 - 5n

Question 2

Answer:

5n + 1

matchsticks[3]

\text{Figure 3:}

16

\text{Figure 4:}

21

\text{Figure 5:}

26

\mathstrut 21 - 16 =

5

Figure

3, 4, 5

: matchsticks

16, 21, 26

, going up by

5

each time.

\mathstrut 16 - 3 \times 5 =

1

5n + 1

matchsticks

Question 3

(a)Answer:

\mathstrut 3 + 3 =

6

[1]

\mathstrut 0 - (-3) =

3

\mathstrut 3 + 3 =

6

(b)Answer:

\mathstrut 50 + 15 =

65

[3]

\mathstrut 26 - 17 =

9

\mathstrut 37 - 26 =

11

\mathstrut 50 - 37 =

13

\mathstrut 11 - 9 =

2

\mathstrut 13 + 2 =

15

\mathstrut 50 + 15 =

65

Question 4

(a)(i)Answer:

\mathstrut 3 + 3 =

6

[1]

\mathstrut 0 - (-3) =

3

\mathstrut 3 + 3 =

6

(a)(ii)Answer:

\mathstrut 54 \times (-3) =

-162

[1]

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

\mathstrut 6 \div (-2) =

-3

\mathstrut 54 \times (-3) =

-162

(b)Answer: YES[2]

\mathstrut 19 - 13 =

6

\mathstrut 13 - 6 =

7

6n + 7 = 139

n = 22

n

is a whole number, so

139

is the 22nd term: Yes.

(c)Answer:

\mathstrut 5 \times 20 + 1 =

101

[3]

\text{Figure 1:}

6

\text{Figure 2:}

11

\text{Figure 3:}

16

\mathstrut 11 - 6 =

5

Figure

1, 2, 3

: matchsticks

6, 11, 16

, going up by

5

each time.

5n + 1

, since Figures

1, 2, 3

have

6, 11, 16

matchsticks

\mathstrut 5 \times 20 + 1 =

101

Question 5

(a)(i)Answer:

\mathstrut 47 + 6 =

53

[1]

\mathstrut 35 - 29 =

6

\mathstrut 47 + 6 =

53

(a)(ii)Answer:

\mathstrut 30 + 9 =

39

[1]

\mathstrut 30 - 21 =

9

\mathstrut 30 + 9 =

39

(b)Answer:

T_n = 7n + 4

[2]

\mathstrut 18 - 11 =

7

\mathstrut 11 - 7 =

4

T_n = 7n + 4

(c)Answer:

\mathstrut 5 \times 100 + 2 =

502

[3]

\text{Figure 2:}

12

\text{Figure 3:}

17

\text{Figure 4:}

22

\mathstrut 17 - 12 =

5

Figure

2, 3, 4

: matchsticks

12, 17, 22

, going up by

5

each time.

5n + 2

, since Figures

2, 3, 4

have

12, 17, 22

matchsticks

\mathstrut 5 \times 100 + 2 =

502

Question 6

(a)Answer:

\mathstrut 16 + 1 \times 5 =

21

[3]

\text{Figure 1:}

6

\text{Figure 2:}

11

\text{Figure 3:}

16

\mathstrut 11 - 6 =

5

Figure

1, 2, 3

: matchsticks

6, 11, 16

, going up by

5

each time.

\mathstrut 16 + 1 \times 5 =

21

(b)(i)Answer:

T_n = 4n + 3

[2]

\mathstrut 11 - 7 =

4

\mathstrut 7 - 4 =

3

T_n = 4n + 3

(b)(ii)Answer: YES[2]

\mathstrut 21 - 13 =

8

\mathstrut 13 - 8 =

5

8n + 5 = 165

n = 20

n

is a whole number, so

165

is the 20th term: Yes.