Syllabus Edition

First teaching 2021

Last exams 2024

|

Sequences (CIE IGCSE Maths: Core)

Exam Questions

2 hours39 questions
1
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2 marks

Find the next term in each of these sequences.

i)
18, 21, 26, 33, 42, .......

[1]

ii)
18, 20, 24, 32, 48, .......

[1]

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2
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1 mark

These are the first four terms of a sequence.

17 10 3 -4
i)
Find the next term.
[1]
ii)
Write down the term to term rule for continuing this sequence.
[1]

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3
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2 marks

Here are the first four terms of a sequence.

32      27      22      17

i)
Write down the next term.
[1]
ii)
Write down the rule for continuing the sequence.
[1]

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4
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2 marks

Write down the next term in each sequence.

i)
12 comma space space space space space space space space space space space space space space space 7 comma space space space space space space space space space space space space space space space space 2 comma space space space space space space space space space space space space space space space space minus 3 comma space space space space space space space space space space space space space space space space minus 8 comma space .....................

[1]

ii)
4 comma space space space space space space space space space space space space space space space space 7 comma space space space space space space space space space space space space space space space space 13 comma space space space space space space space space space space space space space space space space 25 comma space space space space space space space space space space space space space space space 49 comma space.......................

[1]

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5
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1 mark

The diagram shows the first three patterns in a sequence.

q4a-058033-octnov2018-cie-igcse-maths-core

On the grid, draw pattern 4.

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6
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3 marks

These are the first four terms of a sequence.

41        35          29           23

i)
Write down the next two terms.
[2]
ii)
Write down the rule for continuing this sequence.
[1]

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7
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2 marks

These are the first four terms of a sequence.

29 32 35 38

i)
Write down the next term.
[1]
ii)
Write down the rule for continuing this sequence.
[1]

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8
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1 mark

The nth term of a sequence is 5 n space minus space 3.

Write down the first three terms of the sequence.

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9
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2 marks

Find the first three terms of a sequence whose nth term is n squared plus 10.

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10
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2 marks

Here is a sequence.

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

Find the value of a and the value of b.

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

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11
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3 marks

The nth term of a sequence is n cubed minus 5

Write down the first three terms of this sequence.

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12
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2 marks

The nth term of a sequence is n squared space plus space 5.

Find the first three terms of this sequence.

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13
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1 mark

The expression for the nth term of a sequence is 5n squared.

Work out the third term in this sequence.

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1
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2 marks

These are the first four terms of a sequence.

-2 2 6 10

Find an expression for the nth term.

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2
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2 marks

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

5 comma space space space space space space space space space space space space space space space space space space space space 8 comma space space space space space space space space space space space space space space space space space space space space space 11 comma space space space space space space space space space space space space space space space space space space space space 14 comma space                   ....

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3a
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1 mark

These are the first five terms in a sequence.

8          11             14                17                 20

Find the next term.

3b
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2 marks

Find an expression for the nth term.

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4
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1 mark

Write down an expression for the nth term of this sequence.

1             8             27              64

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5a
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1 mark

The nth term of a sequence is 60-8n.

Find the largest number in this sequence.

5b
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2 marks

Here are the first five terms of a different sequence.

12 19 26 33 40

Find an expression for the nth term of this sequence.

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6
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4 marks

The nth term of a sequence is n squared plus 5.

i)
Find the first three terms.
[2]
ii)
Show that 261 is a term in this sequence.
[2]

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7
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2 marks

These are the first four terms of a sequence.

27      33      39      45

Find the nth term of this sequence.

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8
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5 marks

Here are the first three patterns in a sequence.

qp7c-0580-32-paper-3-oct-nov-2019-cie-igcse-maths

i)
Complete the table.
Pattern 1 2 3 4 5
Number of lines 6        

[2]

ii)
Find an expression, in terms of n, for the number of lines in Pattern n.
[2]
iii)
Jake says that he can make one of these patterns using exactly 105 lines.

Explain, without doing any working, why he is wrong.
[1]

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9a
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1 mark

These are the first four terms of a sequence.

5 8 11 14

Write down the next term.

9b
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2 marks

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

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10
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2 marks

These are the first five terms of a sequence.

-4        2         8          14            20

Find an expression for the nth term of this sequence.

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11
Sme Calculator
4 marks

These are the first four terms of a sequence.

8            15             22             29

i)
Find the next term of this sequence.

[1]

ii)
Describe the rule for continuing this sequence.
[1]
iii)
Find an expression for the nth term of this sequence.

[2]

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12
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4 marks

Here are the first four terms of a sequence.

3      9      15      21

i)
Find the next term.
[1]
ii)
Write down the rule for continuing this sequence.
[1]
iii)
Find the nth term of this sequence.
[2]

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13
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2 marks

Find the first three terms of the sequence with nth term n squared plus 5 n.

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14
Sme Calculator
4 marks

These are the first four terms of a sequence.

8 15 22 29
i)
Write down the next term.
[1]
ii)
Write down the term to term rule for continuing this sequence.
[1]
iii)
Find an expression for the nth term.
[2]

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15
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2 marks

The nth term of a sequence is  n squared plus 2 n

Find the first three terms of this sequence.

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1a
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1 mark

A sequence of patterns is made using black counters and white counters.

qp9-0580-33-paper-3-nov-2020-cie-igcse-maths

Draw Pattern 4.

1b
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2 marks

Complete the table.

Pattern 1 2 3 4 5
Number of black counters 4 6 8    
Number of white counters 1 4 9    

1c
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3 marks

Write an expression, in terms of n, for

i)
the number of black counters in Pattern n,
[2]
ii)
the number of white counters in Pattern n.
[1]
1d
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2 marks

Elena has 30 black counters and 140 white counters.

Can she make Pattern 12 using her counters?
Explain your answer.

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2
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2 marks

Gabriela designs the seating layout for a new theatre.

  • There are 12 seats in the front row.
  • Each row has 2 more seats than the row in front of it.

There are 152 seats in the theatre in total.

Work out the number of rows in the theatre.

......................................... rows 

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3a
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5 marks

qp4-0580-33-paper-3-may-2020-cie-igcse-maths

A road has 349 houses on it numbered from 1 to 349.
The diagram shows some of these houses.
The houses on the West side of the road have odd numbers.
The houses on the East side have even numbers.

Tomaz delivers a leaflet to every house on the West side of the road.
He starts at house number 1 and then delivers to each house in order.

i)
Find an expression, in terms of n, for the house number of the nth house he delivers to.
[2]
ii)
Work out the house number of the 40th house he delivers to.
[1]
iii)
Work out how many houses are on the West side of the road.
[2]
3b
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4 marks

Alicia delivers a leaflet to every house on the East side of the road.
She starts at house number 348 and then delivers to each house in order.

i)
Find an expression, in terms of n, for the house number of the nth house she delivers to.
[2]
ii)
What is the largest value of n that can be used in your expression?
Give a reason for your answer.

The largest value of n is .......................... because...............................
[2]

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4a
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1 mark

The grid shows the first three diagrams in a sequence.

Each diagram is made using small squares that are white or grey.

qp8-0580-32-paper-3-march-2020-cie-igcse-maths

On the grid, draw Diagram 4.

4b
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1 mark

Write down the term to term rule for the number of grey squares.

4c
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6 marks
Diagram number 1 2 3 4   n
Number of small white squares 1 4 9      
Number of small grey squares 3 5 7      
Total number of small squares 4 9 16      

Complete the table.

4d
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1 mark

Work out the number of small white squares in Diagram 18.

4e
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2 marks

One of the diagrams has a total of 900 small squares.

Work out its Diagram number.

Diagram ................................................. 

4f
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3 marks

Another diagram has 43 small grey squares.

Work out the total number of small squares in this diagram.

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5
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2 marks

Here is a sequence of numbers.

3,   6,   11,   18,   27,   ...

Find an expression for the nth term of this sequence.

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6
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9 marks

The grid shows the first three diagrams in a sequence.

Each diagram is made using identical small squares.

Each square has sides that are 1 unit long.

q6a-058032-mayjune2019-cie-igcse-maths-core

i)
On the grid, draw Diagram 4.
[1]
ii)
Complete the table.
Diagram number 1 2 3 4
Perimeter 4 12 20  

[1]

iii)
Find an expression, in terms of n, for the perimeter of Diagram n.
[2]
iv)
For one of the diagrams in the sequence the perimeter is 300 units.

Work out its Diagram number.
[2]
v)
Diagram 3 is drawn on a piece of card.
The side of each small square is 7cm.
The diagram is the net of an open box.
Calculate the volume of this box.
Give the units of your answer.
[3]

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7
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9 marks

These are the first four diagrams in a sequence.

Each diagram is made from small equilateral triangles.

q6b-058032-mayjune2019-cie-igcse-maths-core

i)
Write down the number of lines of symmetry of Diagram 3.
[1]
ii)
Complete the table.
Diagram number (n) 1 2 3 4
Number of white triangles (w) 1 3 6  
Number of grey triangles (g) 0   3  
Total number of small triangles (t) 1 4    

iii)
Find a formula, in terms of  n, for the total number of small triangles, t, in Diagram n.

t = ................................................... [1]
iv)
The formula for the number of white triangles, w, in Diagram n is w equals begin inline style 1 half end style n open parentheses n plus 1 close parentheses.
Show that this formula gives the correct number of white triangles when n = 3.
[2]
v)
Complete this statement for Diagram 15.
When n = 15, w = ................. , g = ................. and t = ................. [3]

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8a
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1 mark

Mrs Verma has a restaurant.
In the restaurant each table has 8 chairs.
Sometimes she puts tables together.
The diagrams show how the tables are put together and the position of each chair (X).

q5-058032-march2019-cie-igcse-maths-core

The pattern of tables and chairs forms a sequence.

Draw the diagram for 4 tables.

8b
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2 marks

Complete the table.

Number of tables (t) 1 2 3 4 5 6
Number of chairs (c) 8 10 12      

8c
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2 marks

Find a formula for the number of chairs, c, in terms of the number of tables, t.

c = ............................... 

8d
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2 marks

18 tables are put together in this way.

Work out the number of chairs needed.

8e
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2 marks

Work out the number of tables, put together in this way, when 80 chairs are needed.

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9
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4 marks

These are the first four terms of a sequence.

11         15            19                 23

i)
Write down an expression for the nth term.

[2]

ii)
Is 129 a term in this sequence?
Show how you decide.
............... because ..................................[2]

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10
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6 marks

Each of 196 candidates has a candidate number from 3001 to 3196.

The candidates sit in numerical order in columns and rows, as shown in the diagram.

There are 20 rows.

The diagram shows part of the plan for where the candidates sit.

q2a-058032-march2018-cie-igcse-maths-core

i)
The diagram shows where candidates A and B sit.

Write down their numbers.
A ..................................      
B ..................................  [2]
ii)
Complete this statement.

Candidate 3135 sits in Column .......................... , Row ..........................
[2]
iii)
Candidate C sits in Column n, Row 1.

Find an expression, in terms of n, for the number of candidate C.
[2]

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11a
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1 mark

A sequence of patterns is made using lines and dots.
The first three patterns in the sequence are shown below.

ms5-0580-03-paper-3-specimen-2020-cie-igcse-maths

Draw Pattern 4 on the grid.

11b
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4 marks

Complete the table.

Pattern 1 2 3 4   10
Number of dots 2 3        
Number of lines 4 7        

11c
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3 marks

Find an expression, in terms of n, for

i)
the number of dots in Pattern n,
[1]
ii)
the number of lines in Pattern n.
[2]
11d
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2 marks

A pattern has 76 lines.
Work out how many dots are in this pattern.

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