O Level Cambridge Maths 1 hour 15 questions
Calculator Questions
Sequences
Introduction to Sequences / Types of Sequences / nth Term
Easy (3 questions) /7
Medium (3 questions) /7 Scan here to return to the course
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Hard (6 questions) /26
Very Hard (3 questions) /33
Total Marks /73
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Easy Questions
1 Here is a sequence of numbers.
7, 5, 3, 1, – 1, …
Find the next term in this sequence.
(1 mark)
2 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]
(2 marks)
3 This expression can be used to generate a sequence of numbers.
n 2 − n + 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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(4 marks)
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Medium Questions
1 Find the n th term of the sequence below.
1 1 1 1 1
, , , , , ...
2 4 6 8 10
(1 mark)
2 The n th term of a sequence is 4n 2 + n + 3 .
i) Find the 2nd term.
[1]
ii) Find the value of n when the n th term is 498.
n = .................................................. [3]
(4 marks)
3 Here is a sequence.
a, 13, 9, 3, − 5, − 15, b, ...
Find the value of a and the value of b .
a = ...........................................
b = ...........................................
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(2 marks)
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Hard Questions
1 (a) Find the n th term of each sequence.
4 2 0 -2 -4 ...
(2 marks)
(b) 1 7 17 31 49 ...
(2 marks)
2 Complete the table for the 5th term and the nth term of each sequence.
1st term 2nd term 3rd term 4th term 5th term n th term
9 5 1 -3
4 9 16 25
1 8 27 64
8 16 32 64
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(11 marks)
3 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.
2 4 ........ ........ ........
1 ........ ........ ........ 11
........ −1 ........ ........ 1
(3 marks)
4 Find the n th term of the sequence below.
1, 5, 25, 125, 625, . . .
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(2 marks)
5 Find the n th term of each sequence.
i) −1, − 3, − 5, − 7, − 9, ...
[2]
ii) 2, 9, 28, 65, 126, ...
[2]
(4 marks)
6 Find the n th term of the sequence below.
3, 6, 12, 24, ...
(2 marks)
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Very Hard Questions
1 (a) 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
(2 marks)
(b) Write an expression, in terms of n , for the number of white dots in Diagram n .
(1 mark)
1
(c) The expression for the total number of dots in Diagram n is (3n 2 − n ) .
2
i) Find the total number of dots in Diagram 8.
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[1]
ii) Find an expression for the number of black dots in Diagram n .
Give your answer in its simplest form.
[2]
(3 marks)
(d) T is the total number of dots used to make all of the first n diagrams.
T = an 3 + bn 2
Find the value of a and the value of b .
You must show all your working.
a= ................................................
b= ................................................
(5 marks)
2 The table shows the first four terms in sequences A, B, and C.
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2nd
Sequence 1st term 3rd term 4th term 5th term n th term
term
A 4 9 14 19
B 3 10 29 66
C 1 4 16 64
Complete the table.
(9 marks)
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3 (a) 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.
(3 marks)
(b) Find an expression for the n th term of
i) sequence A,
[2]
ii) sequence B.
[1]
(3 marks)
(c) Find the value of n when the n th term of sequence A is 576.
n = ...............................................
(2 marks)
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(d) i) Find an expression for the n th term of sequence C.
Give your answer in its simplest form.
[3]
ii) Find the value of the 30th term of sequence C.
[2]
(5 marks)
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