New

Year 11

Foundation

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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New

Year 11

Foundation

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.

Download all resources

Share activities with pupils

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Lesson details

Key learning points

The n^th term rule can be generated from the sequence.
The n^th term rule can be generated from the graph.
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.

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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).

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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 $$y=7x-9$$?

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?

$$(-2,-1)$$

$$(-8,-2)$$

$$(22,3)$$

Correct answer: $$(-1,-2)$$

Correct answer: $$(3,22)$$

Q5.

What is the gradient of the line?

$$+3$$

Correct answer: $$+5$$

$$+8$$

$$-5$$

$$-3$$

Q6.

What is the equation of this line?

$$y=x+3$$

$$y=x+5$$

$$y=3x+5$$

Correct answer: $$y=5x+3$$

$$y=5(x+3)$$

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.

line sequences

line segments

line graphs

Correct answer: linear sequences

Q2.

Which term does not belong in this arithmetic sequence?

$$7$$

$$11$$

$$5$$

Correct answer: $$14$$

Q3.

What is the constant additive difference in this linear sequence?

$$-5$$

$$-4$$

$$+2$$

Correct answer: $$+4$$

$$+7$$

Q4.

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

$$(4,-4)$$

$$(-4,4)$$

Correct answer: $$(4,-3)$$

$$(-3,4)$$

$$(5,-7)$$

Q5.

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

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?

$$9-7n$$

$$7-9n$$

Correct answer: $$16-7n$$

$$7n+16$$