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Sequences (Cambridge (CIE) IGCSE Maths: Extended)

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Sequences

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1
Sme Calculator1 mark

Here is a sequence of numbers.

7,   5,   3,   1,   – 1, …

Find the next term in this sequence.

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2
Sme Calculator2 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]

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3
Sme Calculator4 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]

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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

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]

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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........................................... 
b equals........................................... 

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1a
Sme Calculator2 marks

Find the nth term of each sequence.

4        2        0        -2        -4        ...

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1b
Sme Calculator2 marks

1        7        17        31        49        ...

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2
Sme Calculator11 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

 

 

 

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3
Sme Calculator3 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

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4
Sme Calculator2 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...

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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...

 

[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]

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6
Sme Calculator2 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...

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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

 

 

Number of black dots

0

1

3

6

 

 

Total number of dots

1

5

12

22

 

 

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1b
Sme Calculator1 mark

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 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]

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1d
Sme Calculator5 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................................................ 

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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

 

nth term

A

4

9

14

19

 

 

 

B

3

10

29

66

 

 

 

C

1

4

16

64

 

 

 

Complete the table.

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3a
Sme Calculator3 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.

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3b
Sme Calculator3 marks

Find an expression for the nth term of

i) sequence A,  

[2]

ii) sequence B.  

[1]

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3c
Sme Calculator2 marks

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

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.  

[3]

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

[2]

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