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

Arithmetic sequences

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

Expressing an arithmetic sequence

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

a sequence that increases or decreases by the same step 

the constant additive rule from one term to the next

terms that are next to each other in a sequence

initial term $$7$$ and common difference $$-2$$

initial term $$7$$ and common difference $$2$$

initial term $$-1.6$$ and common difference $$0.3$$

initial term $$-1.6$$ and common difference $$-0.3$$

fifth term $$18$$ and common difference $$5$$

ninth term $$-2$$ and common difference $$-5$$

Match the arithmetic sequences with their descriptions. 

$${4\over 5}, {1\over 2}, {1\over 5}, -{1\over 10}, \;$$...

In which of these sequences do the number of shaded squares in each term form a linear sequence?

An arithmetic sequence has 3rd term = 41 and 7th term = 65. What is the initial term?

Which sequences have a constant additive pattern?

Which sequences have a constant multiplicative pattern?

Calculate the perimeter of this rectangle.

Which of these is the area of this rectangle?

What is the term-to-term rule for a sequence with a constant additive pattern which has first term = 23 and  4th term = 41. 

What is the value of $${6\over 7} - 2{1\over2}$$

Arithmetic sequences

Lesson outcome