Cambridge IGCSE · Mathematics (0580)

Sequences: Practice Questions

5 multiple-choice questions marked as you go, and 5 written questions with worked solutions. All on Sequences.

10 questions23 marksFree, no account

Question 1

1 mark

The first four terms of the sequence of triangular numbers are 1, 3, 6, and 10. Find the missing term in the sequence:
1, 3, 6, 10, __, 21, 28

Question 2

1 mark

Find an expression for the \(n\)th term of the sequence:
2, 10, 30, 68, ...

Question 3

1 mark

Find an expression for the \(n\)th term of the quadratic sequence:
5, 12, 23, 38, 57, ...

Question 4

1 mark

The \(n\)th term of a sequence is given by the formula \(T_n = 100 - n^2\).
Calculate the 7th term of this sequence.

Question 5

1 mark

A sequence is formed using a rule similar to the Fibonacci sequence: each term is the sum of the two previous terms.
Given the sequence: 1, 4, 5, 9, 14, ...
Find the next two terms.

Question 6

2 marks

The \(n\)th term of a sequence is given by the formula \(T_n = n^3 + 2\).
Find the value of the 5th term of this sequence.

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Question 7

3 marks

The first term of a sequence is 5. Each subsequent term is found by multiplying the previous term by 2 and then subtracting 3. Calculate the 6th term of this sequence.

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Question 8

5 marks

Find an expression for the \(n\)th term of the following quadratic sequence: \(1, 6, 13, 22, 33, \dots\)

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Question 9

4 marks

Consider the sequence of square numbers 1, 4, 9, 16, ...
(a) Write down the 12th term.
(b) The \(k\)th term of this sequence is 625. Find the value of \(k\).
(c) Find the \(n\)th term of a new sequence 3, 6, 11, 18, ... by comparing it to the square numbers.
(d) Explain why 150 cannot be a term in the sequence of square numbers.

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Question 10

4 marks

Find the \(n\)th term for the sequence 2, 9, 28, 65, ...

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