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Maths Quiz - Level 3-4 Algebra - Sequences (Questions)

Spot patterns in number sequences. Find the term-to-term rule, use nth-term for linear sequences, and recognise non-linear patterns like squares and triangular numbers.

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(quiz starts below)

Fascinating Fact:

If the difference between terms changes, it is called a non-linear sequence, like 1, 4, 9, 16, which are square numbers.

In KS3 Maths, sequences are ordered lists of numbers that follow a rule. You’ll find term-to-term rules, write an nth-term for linear sequences, and recognise non-linear patterns such as squares and triangular numbers.

Key Terms

Term-to-term rule: Instructions to get from one term to the next, e.g. “add 3”.
Nth term: A formula that gives any term directly, like 2n + 1 for odd numbers.
Linear sequence: A sequence with a constant difference between terms (e.g. +4 each time).

Frequently Asked Questions (Click to see answers)

What is the nth term in KS3 maths?

The nth term is a formula that gives any term of a sequence. For example, if the nth term is 3n − 2, the 5th term is 3×5 − 2 = 13.

How can I tell if a sequence is linear?

Check the differences between terms. If the difference is constant (like +5 each time), it’s linear and has an nth term of the form an + b.

How do I find the next terms in a sequence?

Use the rule. If it’s term-to-term, apply it repeatedly. If you have the nth term, substitute the next n values to generate the following terms.

Try These Related Quizzes

1.

An ordered set of numbers that follow a pattern is called what?

[ ]	A Secret
[ ]	A Sequel
[ ]	A Sequence
[ ]	A Sequin

2.

When numbers are put together in such a way that they follow a pattern, they are said to follow a what?

[ ]	Riley
[ ]	Roller
[ ]	Rule
[ ]	Ruler

3.

Each number in a sequence is called a(n) …….

[ ]	Unit
[ ]	Term
[ ]	Item
[ ]	Position

4.

What are the next three numbers in this sequence: 28, 24, 20, 16?

[ ]	14, 12, 10
[ ]	15, 14, 13
[ ]	20, 24, 28
[ ]	12, 8, 4

5.

What are the 3 missing numbers in the following sequence 3, 6, ....... , ....... , ....... , 18, 21, 24?

[ ]	7, 8, 9
[ ]	8, 10, 14
[ ]	9, 12, 15
[ ]	3, 6, 12,

6.

What is the rule in the following sequence 2, 4, 8, 16, 32, 64, 128?

[ ]	Add 8 to the previous number
[ ]	Add together the two previous numbers
[ ]	Double the previous number
[ ]	Halve the previous number

7.

Which numbers come next in the following sequence: 1, 1, 2, 3, 5, 8?

[ ]	13, 21, 34
[ ]	11, 14, 17
[ ]	5, 3, 2
[ ]	12, 20, 30

8.

What is the nth term (Tn) in the sequence 1, 2, 3, 4, 5, …….?

[ ]	9
[ ]	n
[ ]	n + 1
[ ]	n - 1

9.

What is the nth term in this sequence: 4, 7, 10, 13, …….?

[ ]	n + 4
[ ]	3n + 1
[ ]	2n + 2
[ ]	5n - 1

10.

What is the sixth term in the sequence with Tn = 2n - 5?

[ ]	7
[ ]	10
[ ]	17
[ ]	27

You can find more about this topic by visiting BBC Bitesize - Patterns and sequences

Maths Quiz - Level 3-4 Algebra - Sequences (Answers)

1.

An ordered set of numbers that follow a pattern is called what?

[ ]	A Secret
[ ]	A Sequel
[x]	A Sequence
[ ]	A Sequin

A sequence is a particular order in which related things follow each other

2.

When numbers are put together in such a way that they follow a pattern, they are said to follow a what?

[ ]	Riley
[ ]	Roller
[x]	Rule
[ ]	Ruler

The rule might be 'add four' or 'double the last number' for example

3.

Each number in a sequence is called a(n) …….

[ ]	Unit
[x]	Term
[ ]	Item
[ ]	Position

Terms in a sequence are often labelled Tn where n indicates the position of the term in the sequence: for the 1st term, n = 1, for the 2nd n = 2 etc

4.

What are the next three numbers in this sequence: 28, 24, 20, 16?

[ ]	14, 12, 10
[ ]	15, 14, 13
[ ]	20, 24, 28
[x]	12, 8, 4

Each number is 4 less than the previous number. If asked to give the rule we might say 'Take 4 from the previous number'

5.

What are the 3 missing numbers in the following sequence 3, 6, ....... , ....... , ....... , 18, 21, 24?

[ ]	7, 8, 9
[ ]	8, 10, 14
[x]	9, 12, 15
[ ]	3, 6, 12,

The rule is that we add 3 to the previous number

6.

What is the rule in the following sequence 2, 4, 8, 16, 32, 64, 128?

[ ]	Add 8 to the previous number
[ ]	Add together the two previous numbers
[x]	Double the previous number
[ ]	Halve the previous number

If you carried this sequence on the numbers would soon become astronomical!

7.

Which numbers come next in the following sequence: 1, 1, 2, 3, 5, 8?

[x]	13, 21, 34
[ ]	11, 14, 17
[ ]	5, 3, 2
[ ]	12, 20, 30

This sequence is called the Fibonacci sequence. The rule is that we add together the two previous numbers. Sometimes sequences are easy to spot and at other times they take a lot of thinking about!

8.

What is the nth term (Tn) in the sequence 1, 2, 3, 4, 5, …….?

[ ]	9
[x]	n
[ ]	n + 1
[ ]	n - 1

These are simply the counting numbers. The first term is 1; the second term is 2; the third term is 3 etc., so the nth term, Tn, is just n

9.

What is the nth term in this sequence: 4, 7, 10, 13, …….?

[ ]	n + 4
[x]	3n + 1
[ ]	2n + 2
[ ]	5n - 1

Try out each rule to find which fits. If Tn = 3n + 1, when n = 1 the 1st term is 3 x 1 + 1 = 4 but if Tn = n + 4, the 1st term is 1 + 4 = 5

10.

What is the sixth term in the sequence with Tn = 2n - 5?

[x]	7
[ ]	10
[ ]	17
[ ]	27

Use n = 6 to find the value of Tn