IGCSEMathsCambridge (CIE)ExtendedExam QuestionsAlgebra & SequencesSequences

Sequences (Cambridge (CIE) IGCSE Maths: Extended): Exam Questions

Exam code: 0580 & 0980

3 hours39 questions

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Sequences

Easy
Medium
Hard
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1
1 mark

Here is a sequence of numbers.

7,   5,   3,   1,   – 1, …

Find the next term in this sequence.

How did you do?

2
2 marks

Write the next term in each of these sequences.

i) 1    1    2    3    5    8

[1]

ii) 2    4    8    16    32    64

[1]

How did you do?

3
4 marks

This expression can be used to generate a sequence of numbers.

n squared space minus space n plus 11

i) Work out the first three terms of this sequence.

[2]

ii) Show that this expression does not only generate prime numbers.

[2]

How did you do?

1
1 mark

Find the nth term of the sequence below.

1 half comma space space space 1 fourth comma space space space 1 over 6 comma space space space space 1 over 8 comma space space space space 1 over 10 comma space space space space...

How did you do?

2
4 marks

The nth term of a sequence is space 4 n squared plus n plus 3.

i) Find the 2nd term.  

[1]

ii) Find the value of n when the nth term is 498.  

n equals.................................................. [3]

How did you do?

3
2 marks

Here is a sequence.

a comma space space space space space space space 13 comma space space space space space space space space 9 comma space space space space space space space space 3 comma space space space space space space minus 5 comma space space space space space space minus 15 comma space space space space space space space space b comma space space space space space space... space

Find the value of a and the value of b.

a equals........................................... 
b equals........................................... 

How did you do?

4a
1 mark

9 space space space space space space space 12 space space space space space space space 17 space space space space space space space 24 space space space space space space space 33

Write down the next term in the sequence.

How did you do?

4b
3 marks

Find the n to the power of th term of the sequence.

How did you do?

1a
2 marks

Find the nth term of each sequence.

4        2        0        -2        -4        ...

How did you do?

1b
2 marks

1        7        17        31        49        ...

How did you do?

2
11 marks

Complete the table for the 5th term and the nth term of each sequence.

1st term

2nd term

3rd term

4th term

5th term

 

nth term

9

5

1

-3

 

 

 

4

9

16

25

 

 

 

1

8

27

64

 

 

 

8

16

32

64

 

 

 

How did you do?

3
3 marks

0,   1,   1,   2,   3,   5,   8,   13,   21  ,   ...

This sequence is a Fibonacci sequence. After the first two terms, the rule to find the next term is “add the two previous terms”. For example, 5 + 8 = 13.

Use this rule to complete each of the following Fibonacci sequences.

space space space space 2 space space space space space space space space space space space space space space space space 4 space space space space space space space space space space space space space space........ space space space space space space space space space space........ space space space space space space space space space space........ space space space space 1 space space space space space space space space space space space space........ space space space space space space space space space space........ space space space space space space space space space space........ space space space space space space space space space space space space space 11 ........ space space space space space space space space space space minus 1 space space space space space space space space space space space space........ space space space space space space space space space space........ space space space space space space space space space space space space space space 1

How did you do?

4
2 marks

Find the nth term of the sequence below.

1 comma space space space space 5 comma space space space space 25 comma space space space space 125 comma space space space space 625 comma space space space space...

How did you do?

5
4 marks

Find the nth term of each sequence.

i)negative 1 comma space space space space space space space minus 3 comma space space space space space space space minus 5 comma space space space space space space space minus 7 comma space space space space space space space minus 9 comma space space space space space space space...

 

[2]

ii) 2 comma space space space space space space space 9 comma space space space space space space space 28 comma space space space space space space space 65 comma space space space space space space space 126 comma space space space space space space space...  

 

[2]

How did you do?

6
2 marks

Find the nth term of the sequence below.

3 comma space space space space space 6 comma space space space space space 12 comma space space space space space 24 comma space space space space space...

How did you do?

1a
2 marks
cie-igcse-2020-oct-nov-p4-tz1-q7

These are the first four diagrams of a sequence.
The diagrams are made from white dots and black dots.

Complete the table for Diagram 5 and Diagram 6.

Diagram

1

2

3

4

5

6

Number of white dots

1

4

9

16

 

 

Number of black dots

0

1

3

6

 

 

Total number of dots

1

5

12

22

 

 

How did you do?

1b
1 mark

Write an expression, in terms of n, for the number of white dots in Diagram n.

How did you do?

1c
3 marks

The expression for the total number of dots in Diagram n is  1 half open parentheses 3 n squared space minus space n close parentheses.

i) Find the total number of dots in Diagram 8.

[1]

ii) Find an expression for the number of black dots in Diagram n. Give your answer in its simplest form.    

[2]

How did you do?

1d
5 marks

T spaceis the total number of dots used to make all of the first  n diagrams.

T thin space equals space a n to the power of 3 space end exponent plus space b n squared 

Find the value of a and the value of b. You must show all your working.

a space equals ................................................ 

b space equals space................................................ 

How did you do?

2
9 marks

The table shows the first four terms in sequences A, B, and C.

Sequence

1st term

2nd term

3rd term

4th term

5th term

 

nth term

A

4

9

14

19

 

 

 

B

3

10

29

66

 

 

 

C

1

4

16

64

 

 

 

Complete the table.

How did you do?

3a
3 marks

The table shows the first five terms of sequences A, B and C.

Sequence

1st term

2nd term

3rd term

4th term

5th term

6th term

A

0

1

4

9

16

 

B

4

5

6

7

8

 

C

-4

-4

-2

2

8

 

Complete the table.

How did you do?

3b
3 marks

Find an expression for the nth term of

i) sequence A,  

[2]

ii) sequence B.  

[1]

How did you do?

3c
2 marks

Find the value of n when the nth term of sequence A is 576.  

n equals...............................................

How did you do?

3d
5 marks

i) Find an expression for the nth term of sequence C. Give your answer in its simplest form.  

[3]

ii) Find the value of the 30th term of sequence C.  

[2]

How did you do?