An arithmetic (or linear) sequence is a sequence where the difference between successive terms is a constant.

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

Reasoning about values in an arithmetic sequence

Maths

Checking and securing understanding of special number sequences

Fibonacci and alternating sequences

Checking and securing rules for generating arithmetic sequences

Identifying values in an arithmetic sequence

Conditions in arithmetic sequences

Arithmetic sequences and their graphs

Checking and securing understanding of geometric sequences

Problem solving with further sequences

In the prior unit, pupils considered other types of graphs. In this unit, pupils consider different types of sequences such as Fibonacci and oscillating. Their knowledge is consolidated by linking all prior learning together.

In this unit, pupils consider different types of sequences such as Fibonacci and oscillating sequences. They then consolidate their knowledge of different types of sequences by solving contextual problems.

Further sequences

If $$4832$$ is in the sequence $$5n-13$$ then $$5n-13=4832$$ must have a __________.

What is the $$n^\text{th}$$ term rule for the sequence $$-14,-11,-8,-5,-2,1, ...$$?

Yes - the $$n^\text{th}$$ term rule is $$3n-17$$

Yes - the $$n^\text{th}$$ term rule is $$-3n-14$$

No - the $$n^\text{th}$$ term rule is $$3n-17$$

No - the $$n^\text{th}$$ term rule is $$-3n-14$$

Is $$406$$ in the sequence $$-14,-11,-8,-5,-2,1, ...$$?

By explaining that $$1138$$ is even but all positive terms of $$7n-19$$ are odd.

By calculating the first few terms and 'counting on'.

By forming and solving an equation and showing that $$n$$ is not an integer.

By forming and solving an equation and showing that $$n$$ is a positive integer.

How might you show that $$1138$$ is not in the sequence $$7n-19$$?

What is true of the arithmetic sequence $$24, 29, 34, 39, 44, ...$$?

$$707$$ is the $$53^\text{rd}$$ term and $$720$$ the $$54^\text{th}$$ term of an arithmetic sequence. Which of these terms are in the same sequence?

In sequences an $$n^\text{th}$$ term rule is a __________-to-term rule.

Match these sequences to their respective $$n^\text{th}$$ term rules.

What is the $$15^\text{th}$$ term of the sequence $$4n-12$$?

What is the $$15^\text{th}$$ term of the sequence $$12-4n$$?

Solve the equation $$6n-35=331$$  $$n=$${{}}

Solve the equation $$35-6n=-487$$  $$n=$${{}}

Reasoning about values in an arithmetic sequence

Lesson outcome