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New
Year 8

Representing sequences graphically

I can represent arithmetic sequences graphically and appreciate the common structure.

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New
New
Year 8

Representing sequences graphically

I can represent arithmetic sequences graphically and appreciate the common structure.

Link copied to clipboard

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Lesson details

Key learning points

  1. The terms in a sequence can be written as coordinates.
  2. The coordinates can be plotted on a grid.
  3. Arithmetic sequences have common structures.
  4. Other sequences might have common structures you can investigate.

Keywords

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

Common misconception

When plotting sequences, a line must be drawn through the points.

Plot (1,5), (2,10), (3,15), draw a line and find other coordinates. When n = 1.5 the term value is 7.5. Is 7.5 in the sequence 5n??


To help you plan your year 8 maths lesson on: Representing sequences graphically, download all teaching resources for free and adapt to suit your pupils' needs...

Learning cycle 2 sees students looking at the structure of an arithmetic sequence using bricks made up of dots. At this stage ask them to make up a picture of their own sequence and see if they can identify each others' sequences.
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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6 Questions

Q1.
An arithmetic (linear) sequence has a __________ difference.
Correct answer: constant
variable
unknown
positive
Q2.
Which two pairs of coordinates are shown here?
An image in a quiz
$$(1,2)$$ and $$(2,4)$$
$$(1,2)$$ and $$(4,2)$$
$$(2,1)$$ and $$(2,4)$$
Correct answer: $$(2,1)$$ and $$(4,2)$$
Q3.
Match the letters with the correctly plotted coordinates.
An image in a quiz
Correct Answer:A,$$(1,4)$$

$$(1,4)$$

Correct Answer:B,$$(4,1)$$

$$(4,1)$$

Correct Answer:C,$$(4,-1)$$

$$(4,-1)$$

Correct Answer:D,$$(1,-4)$$

$$(1,-4)$$

Q4.
Which of these are true for this sequence?
An image in a quiz
Correct answer: When $$n=1, T=3$$
When $$n=5, T=2$$
Correct answer: When $$n=3, T=7$$
When $$n=5, T=5$$
Correct answer: When $$n=5, T=11$$
Q5.
Match the sequences with the common difference.
Correct Answer:1, 8, 15, 22, ...,+7

+7

Correct Answer:1, -6, -13, -20, ...,-7

-7

Correct Answer:36, 30, 24, 18, ...,-6

-6

Correct Answer:-39, -33, -27, -21, ...,+6

+6

Correct Answer:0, 3, 7, 12, ...,No common difference

No common difference

Correct Answer:-17, -9, -1, 7, ...,+8

+8

Q6.
What is true of this set of coordinates?
An image in a quiz
The $$x$$ coordinate is always double the $$y$$ coordinate.
Correct answer: The $$y$$ coordinate is always double the $$x$$ coordinate.
The $$y$$ coordinate is always two more than the $$x$$ coordinate.
Correct answer: As the $$x$$ coordinate increases by 1, $$y$$ increases by 2

6 Questions

Q1.
When you plot an arithmetic sequence graphically the coordinates form a straight line, hence they are also known as __________ sequences.
additive
Correct answer: linear
straight
common difference
Q2.
If you completed this table of values before plotting the arithmetic sequence $$2n-7$$ which values would you put in the 'Term value' places?
An image in a quiz
Correct answer: -5, -3, -1, 1, 3
-2, 5, 12, 19, 26
-7, -5, -3, -1, 1
-7, -9, -11, -13, -15
-5, -7, -9, -11, -13
Q3.
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?
An image in a quiz
Correct answer: (2,-3)
(-3,2)
Correct answer: (4,5)
(5,4)
Correct answer: (5,9)
Q4.
Which sequence is represented by this graph?
An image in a quiz
Correct answer: $$7-3n$$
$$4-3n$$
$$3n+4$$
$$-5+3n$$
Q5.
This structure represents which sequence?
An image in a quiz
$$3+5n$$
Correct answer: $$3n+5$$
$$(5+3)n$$
Correct answer: $$5+3n$$
$$5n+3$$
Q6.
The sequence $$3n$$ is translated by +6 in the vertical direction. What sequence is now shown?
An image in a quiz
$$n+6$$
$$6n$$
$$6n+3$$
Correct answer: $$3n+6$$
$$9n$$