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      Representing sequences graphically

      Lesson details

      Learning outcome

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

      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??

      Teacher tip

      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.

      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

      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: $$3n+6$$
      $$9n$$

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