New
New
Year 8

# Generating a sequence using a position-to-term rule

I can appreciate that a sequence can be generated and described by a position-to-term rule.

New
New
Year 8

# Generating a sequence using a position-to-term rule

I can appreciate that a sequence can be generated and described by a position-to-term rule.

## Lesson details

### Key learning points

1. The position of a term in the sequence is its term number.
2. The general term can be used to identify a specific term.
3. The general term can be used to generate a sequence .
4. The general term can be used to generate any number in the sequence.
5. The general term can be used to describe a sequence.

### Common misconception

The position-to-term rule is the initial term add the common difference.

Once pupils have found the additive pattern get them to write each term as a value add the difference.

### Keywords

• Position-to-term - A position-to-term rule describes how to generate the term from the term number.

To introduce this lesson, you could give pupils some numbers that form an additive sequence eg 10, 15, 20, 25 and challenge them to write the numbers as repeated addition of 5. They could do this using cuisenaire rods.
Teacher tip

### Licence

This content is © Oak National Academy Limited (2024), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

## Starter quiz

### 6 Questions

Q1.
A term-to term rule describes how to calculate the next term from....
the multiplier
the term number
Q2.
True or false. In the sequence 0, 1, 2, 3, 4, ... the 2nd term is 3.
True- the third number is '2'
Correct answer: False- The second number is not '3'
There is no way of knowing without the term-to-term rule
Q3.
If the 7 times table start with $$1\times 7 = 7$$ what is the 100th number in the 7 times table?
Q4.
Here are the first 3 terms in a pictorial sequence. Which of these rules could refer to the number of lines in each term?
add 2 to the previous term to get the next term
Correct answer: add 3 to the previous term to get the next term
add 5 to the previous term to get the next term
Correct answer: there are 3 lines per section plus 2 for the base.
there are 5 lines per section
Q5.
Which of these is an advantage for using a term-to-term rule
Correct answer: They are easy to use to find the next term in a sequence
They are easy to use to find any term in a sequence
Correct answer: They work for all sequences where there is a rule between successive terms
They are unique, the same rule will always produce the same sequence.
There is only one term-to-term rule that will work if you know the first 3 term.
Q6.
Match the sequences with the term-to-term rules.
Correct Answer:-2, -6, -18, -54, ...,multiply the previous term by 3

multiply the previous term by 3

Correct Answer:-2, -6, -10, -14, ...,add $$-4$$ to the previous term

add $$-4$$ to the previous term

Correct Answer:-2, -6, -14, -30, ...,multiply the previous term by 2 then subtract 2

multiply the previous term by 2 then subtract 2

Correct Answer:-2, -6, -12, -20, ...,add $$-4$$, add $$-6$$, add $$-8$$, ...

add $$-4$$, add $$-6$$, add $$-8$$, ...

Correct Answer:-2, -6, -14, -26, ...,add $$-4$$, add $$-8$$, add $$-12$$, ...

add $$-4$$, add $$-8$$, add $$-12$$, ...

Correct Answer:-2, -6, -8, -8, ...,add $$-4$$, add $$-2$$, add 0, ...

add $$-4$$, add $$-2$$, add 0, ...

## Exit quiz

### 6 Questions

Q1.
Match up the keywords to their definitions
Correct Answer:term,each value or pattern in a sequence

each value or pattern in a sequence

Correct Answer:term-to-term rule,describes how to get from one term to the next

describes how to get from one term to the next

Correct Answer:position-to-term rule,describes how to calculate the term from the term number

describes how to calculate the term from the term number

Correct Answer:sequence ,a succession of values or patterns usually following a rule.

a succession of values or patterns usually following a rule.

Q2.
Using the table shown, match the notation to the term.
Correct Answer:$$T_1$$,3

3

Correct Answer:$$T_2$$,1

1

Correct Answer:$$T_3$$,0

0

Correct Answer:$$T_4$$,-2

-2

Q3.
The position-to-term rule for a sequence is 'multiply the term number by 5 then subtract 10'. What is the 20th term in this sequence?
Q4.
Which of these is a position-to-term rule for the number of dots in each pattern of this sequence?
add 6 to the previous term