What does a child have to do to use a term rule in the 11+?

Use an algebraic rule to calculate a named sequence term. It is one of 55 named maths skills in the 11+, in the algebra strand, and this page carries 1 interactive exercise that practises it.

What is the trap in an 11+ use a term rule question?

The two steps are not interchangeable: multiplying after the second step gives a different value. 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 is not part of use a term rule in the 11+?

The skill map draws the line here: Rule is supplied. 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 use a term rule?

The algebra strand holds 2 skills that are tested together, and the page next to use a term rule is evaluate an algebraic expression. Each has its own exercise and its own link, and none of them needs an account.

How can my child practise use a term rule for free?

Use Function Machine, embedded on this page. It is the exercise the skill map attaches to use a term rule, it runs 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. It also has its own link, so you can send it to a child without sending them anywhere else first.

Maths · Algebra

Use a term rule

Use an algebraic rule to calculate a named sequence term.

Watch the worked example

Open the video page

Unlock Any Sequence Term

This video shows how to use a rule written with letters to calculate a named term in a number sequence. Watch an 11+ maths question solved step by step.

0:00 / 2:25

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Quick quiz: Use a term rule

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

Read the questions in this quiz

Question 1
The rule for this sequence is: multiply the position by 11 then subtract 8. What is the value at position 22?
Term 1
Value
3
Term 2
Value
14
Term 3
Value
25
Term 4
Value
36
Term 5
Value
47
Position Value
Term 1 3
Term 2 14
Term 3 25
Term 4 36
Term 5 47
- A.250
- B.234
- C.242
- D.154
Question 2
The rule for this sequence is: multiply the position by 11 then add 6. What is the value at position 23?
Term 1
Value
17
Term 2
Value
28
Term 3
Value
39
Term 4
Value
50
Term 5
Value
61
Position Value
Term 1 17
Term 2 28
Term 3 39
Term 4 50
Term 5 61
- A.319
- B.247
- C.253
- D.259
Question 3
The rule for this sequence is: multiply the position by 12 then subtract 3. What is the value at position 25?
Term 1
Value
9
Term 2
Value
21
Term 3
Value
33
Term 4
Value
45
Term 5
Value
57
Position Value
Term 1 9
Term 2 21
Term 3 33
Term 4 45
Term 5 57
- A.297
- B.264
- C.300
- D.303
Question 4
The rule for this sequence is: multiply the position by 9 then add 8. What is the value at position 19?
Term 1
Value
17
Term 2
Value
26
Term 3
Value
35
Term 4
Value
44
Term 5
Value
53
Position Value
Term 1 17
Term 2 26
Term 3 35
Term 4 44
Term 5 53
- A.179
- B.243
- C.163
- D.171
Question 5
The rule for this sequence is: multiply the position by 9 then subtract 3. What is the value at position 15?
Term 1
Value
6
Term 2
Value
15
Term 3
Value
24
Term 4
Value
33
Term 5
Value
42
Position Value
Term 1 6
Term 2 15
Term 3 24
Term 4 33
Term 5 42
- A.135
- B.138
- C.132
- D.108
Question 6
The rule for this sequence is: multiply the position by 11 then add 16. What is the value at position 12?
Term 1
Value
27
Term 2
Value
38
Term 3
Value
49
Term 4
Value
60
Term 5
Value
71
Position Value
Term 1 27
Term 2 38
Term 3 49
Term 4 60
Term 5 71
- A.116
- B.148
- C.308
- D.132
Question 7
The rule for this sequence is: multiply the position by 9 then add 14. What is the value at position 12?
Term 1
Value
23
Term 2
Value
32
Term 3
Value
41
Term 4
Value
50
Term 5
Value
59
Position Value
Term 1 23
Term 2 32
Term 3 41
Term 4 50
Term 5 59
- A.234
- B.122
- C.94
- D.108
Question 8
The rule for this sequence is: multiply the position by 11 then add 4. What is the value at position 27?
Term 1
Value
15
Term 2
Value
26
Term 3
Value
37
Term 4
Value
48
Term 5
Value
59
Position Value
Term 1 15
Term 2 26
Term 3 37
Term 4 48
Term 5 59
- A.293
- B.301
- C.297
- D.341
Question 9
The rule for this sequence is: multiply the position by 11 then add 18. What is the value at position 24?
Term 1
Value
29
Term 2
Value
40
Term 3
Value
51
Term 4
Value
62
Term 5
Value
73
Position Value
Term 1 29
Term 2 40
Term 3 51
Term 4 62
Term 5 73
- A.246
- B.462
- C.264
- D.282
Question 10
The rule for this sequence is: multiply the position by 6 then add 17. What is the value at position 19?
Term 1
Value
23
Term 2
Value
29
Term 3
Value
35
Term 4
Value
41
Term 5
Value
47
Position Value
Term 1 23
Term 2 29
Term 3 35
Term 4 41
Term 5 47
- A.97
- B.131
- C.216
- D.114

Position	Value
Term 1	3
Term 2	14
Term 3	25
Term 4	36
Term 5	47

Position	Value
Term 1	17
Term 2	28
Term 3	39
Term 4	50
Term 5	61

Position	Value
Term 1	9
Term 2	21
Term 3	33
Term 4	45
Term 5	57

Position	Value
Term 1	17
Term 2	26
Term 3	35
Term 4	44
Term 5	53

Position	Value
Term 1	6
Term 2	15
Term 3	24
Term 4	33
Term 5	42

Position	Value
Term 1	27
Term 2	38
Term 3	49
Term 4	60
Term 5	71

Position	Value
Term 1	23
Term 2	32
Term 3	41
Term 4	50
Term 5	59

Position	Value
Term 1	15
Term 2	26
Term 3	37
Term 4	48
Term 5	59

Position	Value
Term 1	29
Term 2	40
Term 3	51
Term 4	62
Term 5	73

Position	Value
Term 1	23
Term 2	29
Term 3	35
Term 4	41
Term 5	47

Practise it now

Work out which two gears turn these numbers into those numbers.

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.

Using a supplied term rule

The rule for this sequence is: multiply the position by 3 then add 8. What is the value at position 10?

The table checks the rule: every listed position follows it.

Term 1

Value: 11

Term 2

Value: 14

Term 3

Value: 17

Term 4

Value: 20

Position	Value
Term 1	11
Term 2	14
Term 3	17
Term 4	20

Answer: 38

How you get there

The rule multiplies the position first, so 3 x $10 = 30$ , and adding 8 gives 38, which means position 10 holds 38.

Why the other answers tempt

The two steps are not interchangeable: multiplying after the second step gives a different value.

If they are stuck, say this

Do the multiplication first and the addition second - check the rule on one of the rows in the table before you use it.

Now do it live in Function Machine

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 Use a term rule together. Take a look at the picture. Here is what matters: The table columns are Position, Value. Here comes the question: The rule for this sequence is: multiply the position by 3 then add 8. What is the value at position 10? Before we race ahead, let us choose one good first step. Here is a helpful clue: Do the multiplication first and the addition second - check the rule on one of the rows in the table before you use it. Nice work. Now let us follow the thinking: The rule multiplies the position first, so 3 x 10 = 30, and adding 8 gives 38, which means position 10 holds 38. So our answer is: 38. There is one sneaky trap to watch for: The two steps are not interchangeable: multiplying after the second step gives a different value. 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.

What this exercise is doing

Function Machine

Work out which two gears turn these numbers into those numbers.

A function machine does the same thing to every number that enters it. You found the rule backwards - from the outputs - which is inverse thinking. And the order of the gears is part of the rule: ×3 then +1 turns 2 into 7, while +1 then ×3 turns the same 2 into 9. Same gears, different machine.

Step 1. Deduce the gears. Drag gears into the machine so every ticket comes out right.
Step 2. Run it. New number going in. Predict the output BEFORE you pull the lever.

What to say if they get stuck

Look at 2 → 7 and 4 → 13. When the input goes up by 2, the output jumps by 6. What multiplies by 3?
Try ×3 first: 2 becomes 6, but the ticket says 7. What tiny gear finishes the job?
The order of the gears changes the answer. ×3 then +1 gives 7; +1 then ×3 gives 9.

Open Function Machine on its own page to share it

How use a term rule 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: use an algebraic rule to calculate a named sequence term, and it stops where rule is supplied.

Evaluate an algebraic expression
Substitute one supplied value and calculate the expression. Excludes solving an equation.
Apply a number code rule
Apply one arithmetic mapping to a letter or number code. One invariant rule only.

Questions parents ask about use a term rule

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

: Use an algebraic rule to calculate a named sequence term. It is one of 55 named maths skills in the 11+, in the algebra strand, and this page carries 1 interactive exercise that practises it.
: The two steps are not interchangeable: multiplying after the second step gives a different value. 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. Do the multiplication first and the addition second - check the rule on one of the rows in the table before you use it.
: The skill map draws the line here: Rule is supplied. 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 algebra strand holds 2 skills that are tested together, and the page next to use a term rule is evaluate an algebraic expression. Each has its own exercise and its own link, and none of them needs an account.
: Use Function Machine, embedded on this page. It is the exercise the skill map attaches to use a term rule, it runs 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. It also has its own link, so you can send it 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.