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      Graphing special number sequences using technology

      Lesson details

      Learning outcome

      I can plot the graph of a special number sequence.

      Key learning points

      1. Visual representations of a sequence can help with identification.
      2. Special number sequences can produce interesting graphs.

      Keywords

      • Triangular number - A triangular number (or triangle number) is a number that can be represented by a pattern of dots arranged into a triangle.

      Common misconception

      Pupils may think that given a graph is continuous, the sequence can contain all of the values represented by the line.

      It is important that pupils know when it is appropriate to draw a line to graph sequences and whether values on the line have any meaning. Sequences are often given as a list of terms and without context we cannot assume the sequence is continuous.

      Teacher tip

      Using graphing software can allow pupils to see how a sequence grows and pupils should be encourage to explore what happens when they vary values in the n^th term formula.

      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.
      Which of these are square numbers?

      8
      14
      Correct answer: 16
      26
      Correct answer: 81

      Q2.
      Which of these are cube numbers?

      25
      30
      47
      Correct answer: 64
      100

      Q3.
      Which of these are triangular numbers?

      Correct answer: 10
      16
      22
      Correct answer: 55
      Correct answer: 66

      Q4.
      Which of these is the $$n^{\text{th}}$$ term rule for the linear sequence 6, 10, 14, 18, ...?

      $$n+4$$
      $$n+6$$
      Correct answer: $$4n + 2$$
      $$4n + 6$$
      $$6n + 4$$

      Q5.
      Sam draws a graph of this geometric sequence. Which of these coordinates should Sam plot?

      An image in a quiz
      (1, 5)
      Correct answer: (2, 15)
      (3, 1)
      (3, 15)
      Correct answer: (4, 375)

      Q6.
      Andeep plots the graph of the equation $$y=3.4x-10$$. When the $$y$$ coordinate is $$75$$, the $$x$$ coordinate is .

      Correct Answer: 25

      6 Questions

      Q1.
      The sequence with $$n^{th}$$ term $$5.6n + 12$$ is graphed in the diagram. Is 40 a term in the sequence?

      An image in a quiz
      Correct answer: yes
      no

      Q2.
      The 4th term in the sequence $$3\times 5^{n-1}$$ is . Use Desmos or the diagram to help you.

      An image in a quiz
      Correct Answer: 375

      Q3.
      Is the number 654 in the sequence with $$n^{\text{th}}$$ term rule $$n^3$$? Use Desmos or the diagram to help you.

      An image in a quiz
      Yes, because the two graphs intersect.
      Yes, because $$\sqrt[3]654$$ is an integer.
      Correct answer: No, because the graphs do not intersect at an integer $$x$$ value.
      No, because 654 is not on the curve with equation $$y = n^3$$.

      Q4.
      Why does this diagram not represent the sequence of all square numbers in ascending order?

      An image in a quiz
      Correct answer: The sequence has integer term numbers so the curve should not be drawn.
      This should be a linear graph not a curve.
      The $$y$$ axis scale is double the scale on the $$x$$ axis.
      The square numbers are not on the curve.
      Correct answer: Sequences start when $$n$$ is 1 so there should not be coordinates when $$x<1$$.

      Q5.
      This graph shows the sequence of triangular numbers and the sequence $$4n +4$$ (the line and curve are drawn to help you). Which of these statements are true?

      An image in a quiz
      The number 1 is in both sequences.
      The number 20 is in both sequences.
      Correct answer: The number 28 is in both sequences.
      The 6th term in both sequences is the same.
      Correct answer: The 8th term in both sequences are the same.

      Q6.
      Which is the correct $$n^{\text{th}}$$ term rule for the geometric sequence which starts 1, 2, 4, 8, 16, ...?

      An image in a quiz
      $$2^{n+1}$$
      $$2^n$$
      Correct answer: $$2^n-1$$

      To help you plan your 9 maths lesson on: Graphing special number sequences using technology, download all teaching resources for free and adapt to suit your pupils' needs...