International Maths — Extended

Exam Questions

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- Sets Notes and examples58 questions
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- The four operations Notes and examples
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- Percentages Notes and examples47 questions
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- General requirements154 questions

Sequences (Cambridge International IGCSE Maths): Exam Questions

Exam code:0607

23 questions · 88 marks · ≈ 1 hours

Guided practice

11 markeasy

(a)

These are the first five terms in a sequence.

$811141720$

Find the next term.

Your answer

How did you do?/ 1

22 markseasy

The $n$ th term of a number sequence is $n^{2}+1$

Write down the first three terms of the sequence.

Your answer

How did you do?/ 2

32 markseasy

(b)

Write an expression for the $n$ th term of the sequence below.

15 12 9 6

Your answer

How did you do?/ 2

42 markseasy

(b)

A sequence has $n$ th term $2n^{2}+5n-15$ .
Find the difference between the 4th term and the 5th term of this sequence.

Your answer

How did you do?/ 2

53 marksmedium

1 mark

(a)

In a sequence

$T_{1}=17T_{2}=12T_{3}=7T_{4}=2.$

Find

$T_{5}$

Your answer

2 marks

(b)

Extract:

T_1 = 17 T_2 = 12 T_3 = 7 T_4 = 2.

Find $T_{n}$ .

Your answer

How did you do?/ 3

63 marksmedium

1 mark

(a)

The nth term of a sequence is $60-8n$ . Find the largest number in this sequence.

Your answer

2 marks

(b)

Here are the first five terms of a different sequence.

12 19 26 33 40

Find an expression for the $n$ th term of this sequence.

(2 marks)

Your answer

How did you do?/ 3

72 marksmedium

(b)

Here is a sequence of numbers.

7, 5, 3, 1, – 1, …

Find an expression for the $n$ th term of this sequence.

Your answer

How did you do?/ 2

83 marksmedium

(a)

These are the first four terms of a sequence.

5	8	11	14

i) Write down the next term.

(1 mark)

ii) Find an expression, in terms of n, for the nth term.

(2 marks)

Your answer

How did you do?/ 3

96 marksmedium

2 marks

(a)

19,	15,	11,	7,	....

Write down the next two terms of the sequence.

Your answer

2 marks

(a)

Extract:

19, 15, 11, 7, ....

Find the $n$ th term of this sequence.

(2 marks)

Your answer

2 marks

(a)

Extract:

Find the nth term of this sequence.

Find the value of $n$ when the $n$ th term is -65.

$n$ = ..............................................

Your answer

How did you do?/ 6

102 marksmedium

(b)

These are the first five terms in a sequence.

$811141720$

Find an expression for the $n$ th term.

Your answer

How did you do?/ 2

112 marksmedium

These are the first five terms of a sequence.

$-4281420$

Find an expression for the $n$ th term of this sequence.

Your answer

How did you do?/ 2

126 marksmedium

2 marks

(a)

Marco is making patterns with grey and white circular mats.

cie-igcse-2018-may-jun-1-p4-q12

The patterns form a sequence. Marco makes a table to show some information about the patterns.

Pattern number	1	2	3	4	5
Number of grey mats	6	9	12	15
Total number of mats	6	10	15	21

Complete the table for Pattern 5.

Your answer

2 marks

(b)

Extract:

| Pattern number | 1 | 2 | 3 | 4 | 5 | | Number of grey mats | 6 | 9 | 12 | 15 | |

Find an expression, in terms of $n$ , for the number of grey mats in Pattern $n$ .

Your answer

2 marks

(c)

Extract:

| Pattern number | 1 | 2 | 3 | 4 | 5 | | Number of grey mats | 6 | 9 | 12 | 15 | | | Total number of mats | 6 | 10 | 15 | 21 | |

Marco makes a pattern with 24 grey mats. Find the total number of mats in this pattern.

Your answer

How did you do?/ 6

132 marksmedium

(a)

Find an expression for the $n$ th term of the sequence below.

$11,7,3,-1,...$

Your answer

How did you do?/ 2

142 markshard

(c)

$\frac{1}{3},\frac{3}{4},\frac{4}{7},\frac{7}{11},\frac{11}{18},...$

i) One term of this sequence is $\frac{p}{q}$ .

Find, in terms of $p$ and $q$ , the next term in this sequence.

(1 mark)

ii) Find the 6th term of this sequence.

(1 mark)

Your answer

How did you do?/ 2

151 markhard

(b)

These are the first five terms of a sequence.

$\frac{1}{2}$	$\frac{3}{4}$	$\frac{7}{6}$	$\frac{13}{8}$	$\frac{21}{10}$

Find the next term.

Your answer

How did you do?/ 1

163 markshard

(a)

Find the next term and the $n$ th term of this sequence.

$\frac{3}{5},\frac{4}{7},\frac{5}{9},\frac{6}{11},\frac{7}{13},...$

Next term = .................................................
$n$ th term = .................................................

Your answer

How did you do?/ 3

176 markshard

4 marks

The $n$ th term of a sequence is given by $an^{2}+bn$ where $a$ and $b$ are integers.

The 2nd term of the sequence is —2 The 4th term of the sequence is 12

Find the 6th term of the sequence.

Your answer

2 marks

(b)

Here are the first five terms of a different quadratic sequence.

0 2 6 12 20

Find an expression, in terms of $n$ , for the $n$ th term of this sequence.

Your answer

How did you do?/ 6

183 markshard

1 mark

Find the $n$ th term of each sequence.

4, 8, 12, 16, 20, .........

Your answer

2 marks

11, 20, 35, 56, 83, ..........

Your answer

How did you do?/ 3

196 markshard

1 mark

(a)

Here are the first six terms of a Fibonacci sequence.

1 1 2 3 5 8

The rule to continue a Fibonacci sequence is,

the next term in the sequence is the sum of the two previous terms.

Find the 9th term of this sequence.

Your answer

2 marks

(b)

Extract:

The rule to continue a Fibonacci sequence is, the next term in the sequence is the sum of the two previous terms.

The first three terms of a different Fibonacci sequence are

$aba+b$

Show that the $6$ th term of this sequence is $3a+5b$

Your answer

3 marks

(c)

Extract:

The first three terms of a different Fibonacci sequence are

a b a + b

Show that the 6th term of this sequence is 3a + 5b

Given that the 3rd term is 7 and the 6th term is 29,

find the value of $a$ and the value of $b$ .

Your answer

How did you do?/ 6

203 markshard

These are the first five terms of a sequence.

$2,7,14,23,34$

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

Your answer

How did you do?/ 3

2112 marksvery_hard

10 marks

(a)

Sequence	1st term	2nd term	3rd term	4th term
A	13	9	5	1
B	0	7	26	63
C	$\frac{7}{8}$	$\frac{8}{16}$	$\frac{9}{32}$	$\frac{10}{64}$

Complete the table for the three sequences.

Your answer

2 marks

(b)

Extract:

Sequence C: 7/8, 8/16, 9/32, 10/64

One term in Sequence C is $\frac{p}{q}$ . Write down the next term in Sequence $C$ in terms of $p$ and $q$ .

Your answer

How did you do?/ 12

2210 marksvery_hard

4 marks

(a)

cie-igcse-2019-may-jun-p4-tz2-q11a

The sequence of diagrams above is made up of small lines and dots.

Complete the table.

	Diagram 1	Diagram 2	Diagram 3	Diagram 4	Diagram 5	Diagram 6
Number of small lines	4	10	18	28
Number of dots	4	8	13	19

Your answer

2 marks

(b)

Extract:

For Diagram $n$ find an expression, in terms of $n$ , for the number of small lines.

Your answer

2 marks

(c)

Extract:

For Diagram ![n] find an expression, in terms of ![n], for the number of small lines.

Diagram $r$ has 10 300 small lines. Find the value of $r$ .

$r$ = ..............................................

Your answer

2 marks

(d)

Extract:

| | Diagram 1 | Diagram 2 | Diagram 3 | Diagram 4 | Diagram 5 | Diagram 6 | | Number of small lines | 4 | 10 | 18 | 28 | | | | Number of dots | 4 | 8 | 13 | 19 | | |

The number of dots in Diagram $n$ is $an^{2}+bn+1$ .

Find the value of $a$ and the value of $b$ .

$a$ = ..............................................
$b$ = ..............................................

Your answer

How did you do?/ 10

236 marksvery_hard

2 marks

(a)

The table shows the first five terms of sequence A and sequence B.

Term	1	2	3	4	5	6
Sequence A	7	13	23	37	55
Sequence B	1	3	9	27	81

Complete the table for the 6th term of each sequence.

Your answer

4 marks

(a)

Extract:

The table shows the first five terms of sequence A and sequence B.

| Term | 1 | 2 | 3 | 4 | 5 | 6 | | Sequence A | 7 | 13 | 23 | 37 | 55 | | | Sequence B | 1 | 3 | 9 | 27 | 81 | |

i) Find the $n$ th term of sequence *A. *

(2 marks)

ii) Find the $n$ th term of sequence B.

(2 marks)

Your answer

How did you do?/ 6

Pattern number

Number of grey mats

Total number of mats

Sequence

1st term

2nd term

3rd term

4th term

5th term

nth term

\frac{7}{8}

\frac{8}{16}

\frac{9}{32}

\frac{10}{64}

Diagram 1

Diagram 2

Diagram 3

Diagram 4

Diagram 5

Diagram 6

Number of small lines

Number of dots

Term

Sequence A

Sequence B