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.

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.

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.

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 (2024), 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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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: $$y=5x+3$$
$$y=5(x+3)$$

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: $$16-7n$$
$$7n+16$$