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

Calculating any term

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

Expressing an arithmetic sequence

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 can be used to calculate any term in a sequence so we can call it a __________ for finding the $$n^\text{th}$$ term.

If the $$n^\text{th}$$ term is $$3n+7$$ what are the first five terms?

What is the 5$$^\text{th}$$ term of $$0.3n + 0.07$$?

What are the first five terms of $$10-2n$$?

The 50$$^\text{th}$$ term of the sequence $$2n-1$$.

The 15$$^\text{th}$$ term of the sequence $$6n+10$$.

The 101$$^\text{st}$$ term of the sequence $${1 \over 2} n + 50$$.

The 9$$^\text{th}$$ term of the sequence $$200-11n$$.

Order these term values from lowest to highest.

Which statements are true for the arithmetic sequence $$1.25n-0.3$$?

Which of these words is also used to describe an arithmetic sequence?

Which is the simplified version of $$2 \times a + 5 \times b + 3$$?

If $$a=5$$ and $$b=7$$ what is the value of the expression $$2a+5b+3$$?

Evaluate the expression $$70-3x$$ when $$x=50$$.

Given that $$a=9$$. $$b=-7$$. Put these expressions in order from lowest to highest value.

Starter Quiz

Which of these words is also used to describe an arithmetic sequence?