# 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.

# 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

- Sequences can be created using a rule that tells you how to find the next term from the current one.
- These sequences could be related additively or multiplicity.
- These sequences could be related in other ways.
- This term-to- term method is time consuming when you want to find higher terms in the sequence .
- 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.

### 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).

## Video

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## Starter quiz

### 6 Questions

..., 1, 0.25, ... -

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

..., -8, -20, ... -

add (-12) to the previous term

..., -2, -5, ... -

halve the previous term and subtract 4

..., -6, -14, ... -

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

..., 2, 10, ... -

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

$$4.1\times 0.1$$ -

0.41

$$4.1\div 0.1$$ -

41

$$41\times 10$$ -

410

$$41\times 0.1 $$ -

4.1

$$410\div 0.1$$ -

4100

## Exit quiz

### 6 Questions

8, 12, 18, 27, ... -

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

8, 12, 16, 20, ... -

add 4 to the previous term

8, 12, 20, 32, ... -

add 4, then add 8, then add 12, ...

8, 12, 20, 36, ... -

double the previous term then subtract 4

8, 12, 17, 23, ... -

add 4, then add 5, then add 6, ...