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

Generating a sequence using a position-to-term rule

Maths

The sequences unit allowed pupils to explore different ways of generating sequences and then representing an arithmetic sequence graphically. This serves as an introduction to the future unit on graphical representations of linear equations.

In the prior unit, pupils extended their knowledge of plotting coordinates from KS2 by plotting non-integer values. Pupils learnt that a set of points can satisfy a relationship and this understanding is built on in this unit.

Sequences

describes how to get from one term to the next

describes how to calculate the term from the term number

a succession of values or patterns usually following a rule.

Match up the keywords to their definitions 

Using the table shown, match the notation to the term.

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?

multiply the term number by 6 then add 10

Multiply the term number by 10 then subtract 4

Which of these is a position-to-term rule for the number of dots in each pattern of this sequence?

multiply the term number by 10 then add 2

multiply the term number by 12 and subtract 2

Which of these is a position-to-term rule for the sequence  12, 22, 32, 42, 52, ....

Work out the 100th term in the constant additive sequence which starts: 13, 21, 29, 37, ... The first few lines of working are shown.

A term-to term rule describes how to calculate the next term from....

There is no way of knowing without the term-to-term rule

True or false. In the sequence 0, 1, 2, 3, 4, ... the 2nd term is 3. 

If the 7 times table start with $$1\times 7 = 7$$ what is the 100th number in the 7 times table?

add 2 to the previous term to get the next term

add 3 to the previous term to get the next term

add 5 to the previous term to get the next term

there are 3 lines per section plus 2 for the base. 

Here are the first 3 terms in a pictorial sequence. Which of these rules could refer to the number of lines in each term?

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

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.

Which of these is an advantage for using a term-to-term rule

multiply the previous term by 2 then subtract 2

Match the sequences with the term-to-term rules. 

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