What does a child have to do to continue a number sequence in the 11+?

Infer and apply one arithmetic sequence rule. It is one of 55 named maths skills in the 11+, in the number strand, and this page carries 2 interactive exercises that practise it.

What is the trap in an 11+ continue a number sequence question?

The step has to hold between every pair of rows, not just the first two. The wrong answers on this skill are built out of that, not out of random numbers, so it is worth naming out loud before your child meets it under time pressure.

What can I say if my child is stuck on continue a number sequence?

Point at the next move rather than explaining the whole rule. Compare two rows that sit next to each other to find the step, then check the same step works for every pair.

What is not part of continue a number sequence in the 11+?

The skill map draws the line here: Excludes alternating rules and algebraic nth terms. A question past that line is testing a different named maths skill, which is worth knowing before you spend a week practising the wrong one.

Which other 11+ skills should we practise alongside continue a number sequence?

The number strand holds 13 skills that are tested together, and the pages next to continue a number sequence are divide whole numbers or decimals, evaluate a mixed expression and find a sequence term. Each has its own exercise and its own link, and none of them needs an account.

How can my child practise continue a number sequence for free?

Use Frog Sequence Hop and Number Train, embedded on this page. They are the exercises the skill map attaches to continue a number sequence, they run in the browser with no account to make, these exercises are not scored and do not save learner records. The separate quiz sends answers for marking and shows a score, without saving an assessment record. Each also has its own link, so you can send one to a child without sending them anywhere else first.

Maths · Number

Continue a number sequence

Infer and apply one arithmetic sequence rule.

Watch the worked example

Open the video page

Crack the Sequence Code

This video shows how to find the arithmetic rule in a number sequence and use it to work out the next term. Watch an 11+ maths question solved step by step.

0:00 / 2:44

Turn on captions with the CC button. Jump to any part with the chapter buttons.

Read the transcript

Keep practising with Trace Learn. Find topics to practise next

Quick quiz: Continue a number sequence

10 questions, with feedback after each one. No sign-up needed.

Read the questions in this quiz

Question 1
Priya writes down the first 5 terms of a number sequence. What is the next term?
Term 1
Value
178
Term 2
Value
161
Term 3
Value
144
Term 4
Value
127
Term 5
Value
110
Position Value
Term 1 178
Term 2 161
Term 3 144
Term 4 127
Term 5 110
- A.127
- B.76
- C.110
- D.93
Question 2
Maya writes down the first 5 terms of a number sequence. What is the next term?
Term 1
Value
76
Term 2
Value
93
Term 3
Value
110
Term 4
Value
127
Term 5
Value
144
Position Value
Term 1 76
Term 2 93
Term 3 110
Term 4 127
Term 5 144
- A.178
- B.144
- C.127
- D.161
Question 3
Ivy writes down the first 5 terms of a number sequence. What is the next term?
Term 1
Value
91
Term 2
Value
108
Term 3
Value
125
Term 4
Value
142
Term 5
Value
159
Position Value
Term 1 91
Term 2 108
Term 3 125
Term 4 142
Term 5 159
- A.193
- B.142
- C.159
- D.176
Question 4
Rosa writes down the first 5 terms of a number sequence. What is the next term?
Term 1
Value
43
Term 2
Value
68
Term 3
Value
93
Term 4
Value
118
Term 5
Value
143
Position Value
Term 1 43
Term 2 68
Term 3 93
Term 4 118
Term 5 143
- A.193
- B.143
- C.118
- D.168
Question 5
Rosa writes down the first 5 terms of a number sequence. What is the next term?
Term 1
Value
67
Term 2
Value
75
Term 3
Value
83
Term 4
Value
91
Term 5
Value
99
Position Value
Term 1 67
Term 2 75
Term 3 83
Term 4 91
Term 5 99
- A.99
- B.91
- C.107
- D.115
Question 6
Theo writes down the first 5 terms of a number sequence. What is the next term?
Term 1
Value
161
Term 2
Value
142
Term 3
Value
123
Term 4
Value
104
Term 5
Value
85
Position Value
Term 1 161
Term 2 142
Term 3 123
Term 4 104
Term 5 85
- A.66
- B.47
- C.85
- D.104
Question 7
Noah writes down the first 5 terms of a number sequence. What is the next term?
Term 1
Value
132
Term 2
Value
115
Term 3
Value
98
Term 4
Value
81
Term 5
Value
64
Position Value
Term 1 132
Term 2 115
Term 3 98
Term 4 81
Term 5 64
- A.81
- B.64
- C.30
- D.47
Question 8
Priya writes down the first 5 terms of a number sequence. What is the next term?
Term 1
Value
121
Term 2
Value
109
Term 3
Value
97
Term 4
Value
85
Term 5
Value
73
Position Value
Term 1 121
Term 2 109
Term 3 97
Term 4 85
Term 5 73
- A.61
- B.85
- C.73
- D.49
Question 9
Maya writes down the first 5 terms of a number sequence. What is the next term?
Term 1
Value
105
Term 2
Value
117
Term 3
Value
129
Term 4
Value
141
Term 5
Value
153
Position Value
Term 1 105
Term 2 117
Term 3 129
Term 4 141
Term 5 153
- A.165
- B.141
- C.177
- D.153
Question 10
Omar writes down the first 5 terms of a number sequence. What is the next term?
Term 1
Value
103
Term 2
Value
120
Term 3
Value
137
Term 4
Value
154
Term 5
Value
171
Position Value
Term 1 103
Term 2 120
Term 3 137
Term 4 154
Term 5 171
- A.171
- B.205
- C.154
- D.188

Position	Value
Term 1	178
Term 2	161
Term 3	144
Term 4	127
Term 5	110

Position	Value
Term 1	76
Term 2	93
Term 3	110
Term 4	127
Term 5	144

Position	Value
Term 1	91
Term 2	108
Term 3	125
Term 4	142
Term 5	159

Position	Value
Term 1	43
Term 2	68
Term 3	93
Term 4	118
Term 5	143

Position	Value
Term 1	67
Term 2	75
Term 3	83
Term 4	91
Term 5	99

Position	Value
Term 1	161
Term 2	142
Term 3	123
Term 4	104
Term 5	85

Position	Value
Term 1	132
Term 2	115
Term 3	98
Term 4	81
Term 5	64

Position	Value
Term 1	121
Term 2	109
Term 3	97
Term 4	85
Term 5	73

Position	Value
Term 1	105
Term 2	117
Term 3	129
Term 4	141
Term 5	153

Position	Value
Term 1	103
Term 2	120
Term 3	137
Term 4	154
Term 5	171

Practise it now

The frog can only land on a stone that carries on the pattern. Tap the lily pads to fill both blank stones.

Loading the interactive exercise. Nothing you do here is saved or scored.

A worked example

One question of the kind this skill is tested with, worked all the way through: the reasoning, and what the wrong answers are there to catch.

Finding the step in a sequence

Maya writes down the first 4 terms of a number sequence. What is the next term?

The Position column numbers the terms; the Value column holds them.

Term 1

Value: 22

Term 2

Value: 31

Term 3

Value: 40

Term 4

Value: 49

Position	Value
Term 1	22
Term 2	31
Term 3	40
Term 4	49

Answer: 58

How you get there

Each term is 9 more than the one above it, so the sequence goes up in 9s, which means the term after 49 is 58.

Why the other answers tempt

The step has to hold between every pair of rows, not just the first two.

If they are stuck, say this

Compare two rows that sit next to each other to find the step, then check the same step works for every pair.

Now do it live in Frog Sequence Hop

Kitchen-table script for parents

Try this together

A friendly mini script for the breakfast table, school run or a quiet two minutes. Read it aloud as written, or make it your own.

Ready? Let's have a go at Continue a number sequence together. Take a look at the picture. Here is what matters: The Position column numbers the terms; the Value column holds them. Here comes the question: Maya writes down the first 4 terms of a number sequence. What is the next term? Before we race ahead, let us choose one good first step. Here is a helpful clue: Compare two rows that sit next to each other to find the step, then check the same step works for every pair. Nice work. Now let us follow the thinking: Each term is 9 more than the one above it, so the sequence goes up in 9s, which means the term after 49 is 58. So our answer is: 58. There is one sneaky trap to watch for: The step has to hold between every pair of rows, not just the first two. Can you show me that first move again in your own words? Brilliant. No rush; we are practising a method you can reuse, not trying to win a speed contest.

How each of these 2 exercises teaches it

Frog Sequence Hop

The frog can only land on a stone that carries on the pattern. Tap the lily pads to fill both blank stones.

The trap here is to spot the first gap and assume every gap is the same. From 3 to 6 the gap is 3, but from 6 to 12 the gap is 6, and from 12 to 24 it is 12. When the gaps themselves keep growing, stop adding and start looking for a multiplier: 3 times 2 is 6, 6 times 2 is 12, 12 times 2 is 24, so the sequence doubles and the next terms are 48 and 96. The general strategy for any sequence is to write the differences underneath first. Equal differences mean add the same number every time. Growing differences mean try multiplying, and if that fails try squares or a two-step rule such as double then add one.

What to say if they get stuck

Work out what happens between each pair of stones. Write the jumps down: 3 to 6, 6 to 12, 12 to 24.
The jumps are 3, then 6, then 12. They are not the same size, so this is not an adding sequence.
Each stone is the one before it multiplied by 2. So the next stone is 24 times 2.

Open Frog Sequence Hop on its own page to share it

Number Train

34, 28, 22, 16, 10 … which carriage couples on the end?

This engine’s own main skill is Number Series. It practises continue a number sequence alongside it, and covers most of it rather than all.

Look at the couplings, not the carriages. The gaps between 34, 28, 22, 16, 10 are -6, -6, -6, -6 - and that is where the pattern lives: every coupling takes away 6. Carrying it on from 10 gives 4.

What to say if they get stuck

Press Roll - the ball hops between carriages and writes the gap into each coupling.
Every gap is the same size. Add it once more to the last carriage.

Open Number Train on its own page to share it

How continue a number sequence differs from the skills beside it

The same exercise practises several skills, and telling them apart is often the difficulty rather than the exercise itself. On this page the skill is: infer and apply one arithmetic sequence rule, and it stops where excludes alternating rules and algebraic nth terms.

Find a sequence term
Use a stated or inferred linear rule to find a named term. One linear sequence only.
Follow alternating code rules
Continue a code whose two explicit rules alternate. Exactly two repeating rules.
Continue a letter or number sequence
Infer and apply one or two repeating symbolic rules. Record rule count and alternation separately.

Related maths skills

Add whole numbers or decimalsCalculate one addition with aligned place values.
Calculate a whole-number operationCalculate one stated addition, subtraction, multiplication, or division.
Compare and order numbersOrder or compare a bounded set of integers or decimals.
Divide whole numbers or decimalsCalculate one division and interpret any remainder as stated.
Evaluate a mixed expressionApply operation order to a supplied numerical expression.
Multiply whole numbers or decimalsCalculate one multiplication using place-value reasoning or a written method.
Read place valueState the value of one digit in an integer or decimal.
Round to a stated placeRound one integer or decimal to the stated place value.
Scale by a power of tenMultiply or divide a number by 10, 100, or 1000 using place value.
Solve a one-step number problemChoose and perform one operation in a short context.
Subtract whole numbers or decimalsCalculate one subtraction with aligned place values.

All maths 11+ skills

Questions parents ask about continue a number sequence

What this skill involves, common mistakes and ways to practise it at home.

: Infer and apply one arithmetic sequence rule. It is one of 55 named maths skills in the 11+, in the number strand, and this page carries 2 interactive exercises that practise it.
: The step has to hold between every pair of rows, not just the first two. The wrong answers on this skill are built out of that, not out of random numbers, so it is worth naming out loud before your child meets it under time pressure.
: Point at the next move rather than explaining the whole rule. Compare two rows that sit next to each other to find the step, then check the same step works for every pair.
: The skill map draws the line here: Excludes alternating rules and algebraic nth terms. A question past that line is testing a different named maths skill, which is worth knowing before you spend a week practising the wrong one.
: The number strand holds 13 skills that are tested together, and the pages next to continue a number sequence are divide whole numbers or decimals, evaluate a mixed expression and find a sequence term. Each has its own exercise and its own link, and none of them needs an account.
: Use Frog Sequence Hop and Number Train, embedded on this page. They are the exercises the skill map attaches to continue a number sequence, they run in the browser with no account to make, these exercises are not scored and do not save learner records. The separate quiz sends answers for marking and shows a score, without saving an assessment record. Each also has its own link, so you can send one to a child without sending them anywhere else first.

Knowing which maths topic to practise is most of the work

A free diagnostic covers arithmetic, fractions, geometry, measure and data handling, and comes back with the topics to spend the next few weeks on.