IGCSEMaths: ExtendedCIETopic QuestionsAlgebra & SequencesSequences

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First teaching 2023

First exams 2025

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Sequences (CIE IGCSE Maths: Extended)

Topic Questions

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1
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Here is a sequence of numbers.

7,Ā  Ā 5,Ā  Ā 3,Ā  Ā 1,Ā  Ā ā€“ 1, ā€¦

Find the next term in this sequence.

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2
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Write the next term in each of these sequences.

i)
1 Ā Ā Ā 1Ā Ā Ā  2 Ā Ā Ā 3 Ā Ā Ā 5 Ā Ā Ā 8

[1]

ii)
2 Ā Ā Ā 4 Ā Ā Ā 8 Ā Ā Ā 16 Ā Ā Ā 32 Ā Ā Ā 64

[1]

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3
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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]

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1a
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Find the nth term of each sequence.

4 Ā  Ā  Ā  Ā 2 Ā  Ā  Ā  Ā 0 Ā  Ā  Ā  Ā -2 Ā  Ā  Ā  Ā -4 Ā  Ā  Ā  Ā ...



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1b
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1 Ā  Ā  Ā  Ā 7 Ā  Ā  Ā  Ā 17 Ā  Ā  Ā  Ā 31 Ā  Ā  Ā  Ā 49 Ā  Ā  Ā  Ā ...

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2
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Complete the table for the 5th term and the nth term of each sequence.

1st term 2nd term 3rd term 4th term 5th term Ā  nth term
9 5 1 -3 Ā  Ā  Ā 
4 9 16 25 Ā  Ā  Ā 
1 8 27 64 Ā  Ā  Ā 
8 16 32 64 Ā  Ā  Ā 

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

This sequence is a Fibonacci sequence.
After the first two terms, the rule to find the next term is ā€œadd the two previous termsā€.
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

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4
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Find theĀ 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...

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5
Sme Calculator4 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...
Ā 
Ā 

[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...
Ā 
Ā 

[2]

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6
Sme Calculator2 marks

Find theĀ 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...

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1
Sme Calculator1 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...

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2
Sme Calculator4 marks

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

i)

Find the 2nd term.
Ā 

[1]

ii)

Find the value ofĀ n when the nth term is 498.
Ā 

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

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3
Sme Calculator2 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...........................................Ā 
b equals...........................................Ā 

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1a
Sme Calculator2 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 Ā  Ā 
Number of black dots 0 1 3 6 Ā  Ā 
Total number of dots 1 5 12 22 Ā  Ā 

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1b
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Write an expression, in terms of n, for the number of white dots in Diagram n.

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1c
Sme Calculator3 marks

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

i)
Find the total number of dots in Diagram 8.
Ā  Ā 
[1]
ii)
Find an expression for the number of black dots in Diagram n.
Give your answer in its simplest form.
Ā  Ā 
[2]

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1d
Sme Calculator5 marks

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

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

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


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

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

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2
Sme Calculator9 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 Ā  nth term
A 4 9 14 19 Ā  Ā  Ā 
B 3 10 29 66 Ā  Ā  Ā 
C 1 4 16 64 Ā  Ā  Ā 


Complete the table.

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3a
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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 Ā 
B 4 5 6 7 8 Ā 
C -4 -4 -2 2 8 Ā 

Complete the table.

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3b
Sme Calculator3 marks

Find an expression for the nth term of

i)

sequenceĀ A,
Ā 

[2]

ii)

sequenceĀ B.
Ā 

[1]

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3c
Sme Calculator2 marks

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

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

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3d
Sme Calculator5 marks

i)

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

[3]

ii)

Find the value of the 30th term of sequence C.
Ā 

[2]

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