New
New
Lesson 7 of 12
  • Year 11
  • Higher

Arithmetic sequences and their graphs

I can recognise that an arithmetic sequence can be shown graphically and how this relates to the equation of a linear graph and use this to find the n^th term formula.

Lesson 7 of 12
New
New
  • Year 11
  • Higher

Arithmetic sequences and their graphs

I can recognise that an arithmetic sequence can be shown graphically and how this relates to the equation of a linear graph and use this to find the n^th term formula.

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Lesson details

Key learning points

  1. The n^th term rule can be generated from the sequence.
  2. The n^th term rule can be generated from the graph.
  3. The n^th term rule is the equation of the line.

Keywords

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

  • N^th term - The n^th term of a sequence is the position of a term in a sequence where n stands for the term number.

Common misconception

When plotting a sequence you should always connect the points with a line.

Only the (term number, term value) should be plotted. Points should not be joined as these are discrete values.


To help you plan your year 11 maths lesson on: Arithmetic sequences and their graphs, download all teaching resources for free and adapt to suit your pupils' needs...

Knowing the shape of the graph for arithmetic sequences means pupils have a way of checking any terms generated as the values should align.
Teacher tip

Licence

This content is © Oak National Academy Limited (2025), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

Lesson video

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Prior knowledge starter quiz

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6 Questions

Q1.
Arithmetic sequences have a __________ difference between successive terms.

positive
negative
Correct answer: constant
variable

Q2.
Which of these will be amongst the first five terms of the arithmetic sequence $$3n-2$$?

$$-2$$
Correct answer: $$1$$
$$3$$
Correct answer: $$4$$
$$5$$

Q3.
Which values are missing from this table for the linear equation $$y=7x-9$$?

An image in a quiz
Correct answer: $$-2$$
$$-1$$
$$2$$
$$17$$
Correct answer: $$19$$

Q4.
Here is a table of values for the linear equation $$y=6x-4$$ When graphing this equation which coordinate pairs would you plot?

An image in a quiz
$$(-2,-1)$$
$$(-8,-2)$$
$$(22,3)$$
Correct answer: $$(-1,-2)$$
Correct answer: $$(3,22)$$

Q5.
What is the gradient of the line?

An image in a quiz
$$+3$$
Correct answer: $$+5$$
$$+8$$
$$-5$$
$$-3$$

Q6.
What is the equation of this line?

An image in a quiz
$$y=x+3$$
$$y=x+5$$
$$y=3x+5$$
Correct answer: $$y=5x+3$$
$$y=5(x+3)$$

Assessment exit quiz

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6 Questions

Q1.
Arithmetic sequences like this one are also called ________ because they increase or decrease in a straight line.

An image in a quiz
line sequences
line segments
line graphs
Correct answer: linear sequences

Q2.
Which term does not belong in this arithmetic sequence?

An image in a quiz
$$7$$
$$11$$
$$5$$
Correct answer: $$14$$

Q3.
What is the constant additive difference in this linear sequence?

An image in a quiz
$$-5$$
$$-4$$
$$+2$$
Correct answer: $$+4$$
$$+7$$

Q4.
What is the next coordinate pair we would plot when graphing this arithmetic sequence?

An image in a quiz
$$(4,-4)$$
$$(-4,4)$$
Correct answer: $$(4,-3)$$
$$(-3,4)$$
$$(5,-7)$$

Q5.
What is the $$n^\text{th}$$ term of the arithmetic sequence graphed here?

An image in a quiz
Correct answer: $$2n-3$$
$$2n-1$$
$$-1n+2$$
$$n+2$$
$$3n-2$$

Q6.
What is the $$n^\text{th}$$ term of the arithmetic sequence graphed here?

An image in a quiz
$$9-7n$$
$$7-9n$$
Correct answer: $$16-7n$$
$$7n+16$$