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

Finding the nth  term

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

5$$n$$ - 2 is the __________ of the sequence 3, 8, 13, 18, ...

To find the $$n^\text{th}$$ term of an arithmetic sequence, which of the following do we need?

17, 21, 25, 29, ... is a translation of what from the sequence 4$$n$$?

What is the $$n^\text{th}$$ term of the arithmetic sequence 10, 15, 20, 25, ...?

The sequence $$17-7n$$ has a common difference of what?

Find the $$n^\text{th}$$ term of the sequence 2.31, 2.22, 2.13, 2.04, ...

The n$$^\text{th}$$ term is the position of a term in a sequence ($$n$$ is the term number). It can be used to calculate any term so is also known as a __________ for finding the n$$^\text{th}$$ term.

What is the term-to-term rule for this pattern sequence?

What is the position-to-term rule for this pattern sequence?

Which of these are arithmetic (linear) sequences?

$$4 + 4 + 4 + 4 + 4 + \;$$... fifty times.

This pattern represents people seated around an increasing number of tables. If you were asked to find the number of people around 50 tables, which calculation would you do?

Order these arithmetic sequences in terms of the size of their common difference. Start with the greatest common difference.

This lesson will be removed by end of Summer Term 2025.

Finding the nth term

Lesson outcome

This lesson will be removed by end of Summer Term 2025.