Cambridge IGCSE · International Mathematics (0607)

Sequences: Practice Questions

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

10 questions24 marksFree, no account

Question 1

1 mark

Consider the following sequence of numbers:
2, 5, 8, 11, ...

Find the next term in this sequence.

Question 2

1 mark

A sequence of shapes is made using small squares. Shape 1 uses 3 squares, Shape 2 uses 8 squares, and Shape 3 uses 15 squares. If this pattern continues, find an expression for the number of squares in Shape \(n\).

Question 3

1 mark

Find the \(n^{th}\) term of the sequence: 0, 4, 20, 54, 112, ...

Question 4

1 mark

A sequence is defined by the following terms:
5, 11, 19, 29, 41, ...

By finding the first and second differences, determine the expression for the \(n^{th}\) term of this quadratic sequence.

Question 5

1 mark

Consider the sequence: 0, 10, 28, 54, 88, ...

By finding the first and second differences, find an expression for the \(n^{th}\) term of this sequence.

Question 6

2 marks

Write down the next two terms in the following sequence:
2, 5, 8, 11, ...

Write your answer out first, then check it against the worked solution.

Question 7

3 marks

Find the \( n^{\text{th}} \) term expression for the following linear sequence:
\( -2, 1, 4, 7, \dots \)

Write your answer out first, then check it against the worked solution.

Question 8

5 marks

Consider the sequence whose first four terms are:
1, 14, 51, 124, ...

Find an expression for the \(n^{th}\) term of this sequence.

Write your answer out first, then check it against the worked solution.

Question 9

5 marks

A pattern of squares is made using sticks as follows:

Pattern 1: 1 square (4 sticks)
Pattern 2: 2 squares in a row (7 sticks)
Pattern 3: 3 squares in a row (10 sticks)

(a) Find the number of sticks needed for Pattern 5.
(b) Determine the n^th term rule for the number of sticks, \(S_n\), in Pattern \(n\).
(c) Calculate the number of sticks needed for Pattern 50.
(d) A pattern uses 121 sticks. Find the number of squares in this pattern.

Write your answer out first, then check it against the worked solution.

Question 10

4 marks

The first four terms of an exponential sequence are 5, 15, 45, 135, ...

(a) Find the common ratio.
(b) Find an expression for the \(n^{\text{th}}\) term, \(T_n\).
(c) Find the smallest value of \(n\) for which the term is greater than 10,000.

Write your answer out first, then check it against the worked solution.

* The content provided by thinka is generated by AI and may not always be accurate or up-to-date. Please use it as a supplementary resource and verify with official materials.

You've seen the model answer. Now get yours marked.

This page can show you how a good answer looks. It cannot tell you what your answer was missing. thinka marks your written work against the real mark scheme in about 15 seconds.

Get My Answers Marked Back to the notes

Want more questions like these? Get a fresh set on this topic, marked as you go.