New
New
Year 8

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

I can appreciate that a sequence can be generated and described using term-to-term approaches.

New
New
Year 8

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

I can appreciate that a sequence can be generated and described using term-to-term approaches.

## Lesson details

### Key learning points

1. Sequences can be created using a rule that tells you how to find the next term from the current one.
2. These sequences could be related additively or multiplicity.
3. These sequences could be related in other ways.
4. This term-to- term method is time consuming when you want to find higher terms in the sequence .
5. It is possible to describe the rule when given some of the terms although this may not be unique.

### Common misconception

The difference in the given terms divided by the number of missing terms gives the common difference

Write the sequence out with gaps for the missing terms. Model how many additions (jumps) to get from one known term to the next.

### Keywords

• Term-to-term - A term-to-term rule describes how to calculate the next term in the sequence from the previous term.

This is a good opportunity to practise arithmetic with fractions and negatives. This reinforces concepts like 'subtracting a negative is the same as adding the absolute value' and 'dividing by a fraction is the same as multiplying by its reciprocal.'
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.
Which of these best describes what a term in a sequence is?
The number of patterns in a sequence
The first number in a sequence
The multiplier to get from one value to the next
The difference between successive values
Correct answer: An individual diagram or value in a sequence
Q2.
What would be the next value in this sequence if it has a constant additive rule? -1, 6, , ...
Q3.
What would be the next value in this sequence if it has a constant multiplicative rule? -1, 6, , ...
Q4.
Match the next 2 numbers in the sequence which starts 16, 4, ... with the rule the sequence is following.
Correct Answer:..., 1, 0.25, ...,Multiply the previous term by $$1\over 4$$

Multiply the previous term by $$1\over 4$$

add (-12) to the previous term

Correct Answer:..., -2, -5, ...,halve the previous term and subtract 4

halve the previous term and subtract 4

Correct Answer:..., -6, -14, ...,subtract 12, then subtract 10, then subtract 8 ...

subtract 12, then subtract 10, then subtract 8 ...

Correct Answer:..., 2, 10, ...,subtract 12, then subtract 2, then subtract -8 ...

subtract 12, then subtract 2, then subtract -8 ...

Q5.
Calculate the number halfway between 16 and 34
Q6.
Match these calculations to the correct answers.
Correct Answer:$$4.1\times 0.1$$,0.41

0.41

Correct Answer:$$4.1\div 0.1$$,41

41

Correct Answer:$$41\times 10$$,410

410

Correct Answer:$$41\times 0.1$$,4.1

4.1

Correct Answer:$$410\div 0.1$$,4100

4100

## Exit quiz

### 6 Questions

Q1.
Which of these best describes what a term-to-term rule is?
A rule to find any term in a sequence
A rule to find the first term in a sequence
Correct answer: A rule to find the next term in a sequence from the previous term
A rule to find the multiplier for a sequence
A rule to find the constant additive pattern for a sequence
Q2.
Match the term-to-term rules with the sequences
Correct Answer:8, 12, 18, 27, ...,multiply the previous term by $$3\over 2$$

multiply the previous term by $$3\over 2$$

add 4 to the previous term

Correct Answer:8, 12, 20, 36, ...,double the previous term then subtract 4

double the previous term then subtract 4

Q3.
A sequence starts 7,10, ... What is the 10th term if the term to term rule is 'add 3 to the previous term'?
Q4.
Which of the statements below is a limitation of using term-to-term rules?
Correct answer: They can be time consuming or complex to use when finding a larger term number.
They can be difficult to use when you want to find the next term.
Correct answer: Different sequences can be made from the same rule with different 1st terms.
Correct answer: Different rules can apply to the same few terms.
They only work for constant additive patterns.
Q5.
What is the term-to-term rule for this sequence with a constant additive pattern? 17, ?, 29, ?, 41, ...
Correct answer: add $$6$$ to the previous term
add $$11$$ to the previous term
add $$12$$ to the previous term
add $$17$$ to the previous term
add $$24$$ to the previous term
Q6.
What is the term-to-term rule for the constant additive sequence with 2nd term = 63 and 7th term = 23?
add $$-10$$ each time
Correct answer: add $$-8$$ each time
add $$-5$$ each time
add $$8$$ each time
add $$40$$ each time