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

Representing sequences graphically

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

Calculating any term

Finding the nth  term

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

When you plot an arithmetic sequence graphically the coordinates form a straight line, hence they are also known as __________ sequences.

If you completed this table of values before plotting the arithmetic sequence $$2n-7$$ which values would you put in the 'Term value' places?

This is a table of values for the sequence $$4n-11$$. If you were going to graph this sequence which of these coordinates are correct?

Which sequence is represented by this graph?

This structure represents which sequence?

The sequence $$3n$$ is translated by +6 in the vertical direction. What sequence is now shown?

An arithmetic (linear) sequence has a __________ difference.

Which two pairs of coordinates are shown here?

Match the letters with the correctly plotted coordinates.

Which of these are true for this sequence?

Match the sequences with the common difference.

The $$x$$ coordinate is always double the $$y$$ coordinate.

The $$y$$ coordinate is always double the $$x$$ coordinate.

The $$y$$ coordinate is always two more than the $$x$$ coordinate.

As the $$x$$ coordinate increases by 1, $$y$$ increases by 2

Representing sequences graphically

Lesson outcome