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

Generating a sequence using a term-to-term rule

Maths

Checking understanding of sequences

Securing understanding of sequences

Formalising a sequence

Generating a sequence using a position-to-term rule

Arithmetic sequences

Expressing an arithmetic sequence

Calculating any term

Finding the nth  term

Representing sequences graphically

Justifying terms of a sequence

Problem solving with sequences

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.

In this unit we develop knowledge of sequences to be able to identify, determine, and continue arithmetic sequences. We finish the unit by looking at how sequences may be reprsented graphically.

Sequences

A rule to find the first term in a sequence

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 

Which of these best describes what a term-to-term rule is?

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

Match the term-to-term rules with the sequences

A sequence starts 7,10, ... What is the 10th term if the term to term rule is 'add 3 to the previous term'?

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. 

Different sequences can be made from the same rule with different 1st terms.

Different rules can apply to the same few terms.

They only work for constant additive patterns. 

Which of the statements below is a limitation of using term-to-term rules?

What is the term-to-term rule for this sequence with a constant additive pattern?  17, ?, 29, ?, 41, ...

What is the term-to-term rule for the constant additive sequence with 2nd term = 63 and 7th term = 23?

The multiplier to get from one value to the next

An individual diagram or value in a sequence

Which of these best describes what a term in a sequence is?

What would be the next value in this sequence if it has a constant additive rule? -1, 6, {{}}, ...

What would be the next value in this sequence if it has a constant multiplicative rule? -1, 6, {{}}, ...

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

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

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

Match the next 2 numbers in the sequence which starts 16, 4, ... with the rule the sequence is following. 

Calculate the number halfway between 16 and 34

Match these calculations to the correct answers. 

Generating a sequence using a term-to-term rule

Lesson outcome