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, nothing is scored, and nothing a child does here is recorded or sent anywhere. 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.

Free to use and free to share. There is no sign-up, no score, and nothing a child does here is recorded or sent anywhere.

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.

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

67
58
49
40

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

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

All maths 11+ skills

Questions parents ask about continue a number sequence

Answered from what the skill map records about this skill, not from a template. Every answer here is on the page, and the same questions are the page's FAQ structured data.

: 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, nothing is scored, and nothing a child does here is recorded or sent anywhere. 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.

Start the free 11+ diagnostic