The n^th term of a sequence is the position of a term in a sequence where n stands for the term number.

Expressing an arithmetic sequence

Maths

Checking understanding of sequences

Securing understanding of sequences

Formalising a sequence

Generating a sequence using a term-to-term rule

Generating a sequence using a position-to-term rule

Arithmetic sequences

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

The $$n^\text{th}$$ term of a sequence is the position of a term in a sequence where $$n$$ stands for the term {{}}.

In this sequence when $$n=4$$ what is the term value?

In this sequence when $$T=4$$ what is the term number?

What general rule links pattern number ($$n$$) to number of squares ($$T$$) in this case?

What general rule links pattern number ($$n$$) to the perimeter of each shape?

How to generate the term from the term number

How many positions there are in a sequence

In sequences, a position-to-term rule describes what?

Multiplying $$x$$ by 4 and subtracting 7 is most simply written as which expression?

Which position-to-term rule satisfies this sequence?

Multiply the pattern number by 3 then add 1.

Multiply the pattern number by 3 then subtract 1.

Which position-to-term rule links the pattern number to the number of squares?

For the arithmetic sequence starting 1, 4, 7, 10, 13, ... the position-to-term rule is 'multiply by 3 and subtract 2'. What therefore, is the 100$$^\text{th}$$ term?

Substitute the value $$a=6$$ into the below expressions. Order the value of the expressions from highest to lowest.

Starter Quiz

In sequences, a position-to-term rule describes what?