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      Representing geometric sequences graphically

      Lesson details

      Learning outcome

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

      Key learning points

      1. A geometric sequence looks like a curve when sketched (common ratio > 1 or < 1).
      2. The gradient increases sharply (common ratio > 1 or < 1).
      3. Although the graph is continuous, the sequence is not.
      4. Each geometric sequence is made up of discrete terms.

      Keywords

      • Geometric sequence - A geometric sequence is a sequence with a constant multiplicative relationship between successive terms.

      • Common ratio - A common ratio is a key feature of a geometric sequence. The constant multiplier between successive terms is called the common ratio.

      Common misconception

      Pupils may thing that given the 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

      It is great for pupils to explore graphs of geometric sequences with common ratios that they choose, ideally using graphing software.

      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 type of sequence is represented by this graph?

      An image in a quiz
      Correct answer: arithmetic
      geometric
      Correct answer: linear
      non-linear
      quadratic

      Q2.
      How can you tell that the sequence 17, 24, 31, 38, 45, ... is arithmetic?

      It is increasing.
      It has no negative terms.
      Correct answer: It has a common additive difference between successive terms.
      It has a constant multiplicative relationship between successive terms.

      Q3.
      How can you tell that the sequence 0.02, 0.2, 2, 20, 200, ... is geometric?

      It is increasing.
      It has no negative terms.
      It has a common additive difference between successive terms.
      Correct answer: It has a constant multiplicative relationship between successive terms.

      Q4.
      Sofia plots the graph of this arithmetic sequence. Which of these coordinates should Sofia plot?

      An image in a quiz
      Correct answer: (1, 21)
      (21, 1)
      (18, 15)
      Correct answer: (3, 15)
      (18, 2)

      Q5.
      Which of these will be one of the first five terms in the geometric sequence that has a first term of 1.25 and a common ratio of 2?

      0.625
      Correct answer: 2.5
      3.25
      Correct answer: 10
      Correct answer: 20

      Q6.
      The missing $$2^{\text{nd}}$$ term of this geometric sequence is .

      An image in a quiz
      Correct Answer: 96000, 96 000, ninety six thousand, 96,000

      6 Questions

      Q1.
      This graph of $$n$$ (term number) against $$T$$ (term value) could represent which of these types of sequences?

      An image in a quiz
      linear
      Correct answer: geometric
      arithmetic
      additive

      Q2.
      Jacob plots the graph of this geometric sequence. Which coordinates should Jacob plot?

      An image in a quiz
      (30, 150)
      (30, 2)
      Correct answer: (2, 30)
      (750, 4)
      Correct answer: (4, 750)

      Q3.
      How do you know that this graph might represent a geometric sequence?

      An image in a quiz
      The points form a straight line.
      The graph is increasing.
      The terms are all positive.
      Correct answer: The points form a curve.

      Q4.
      What do you know about the common ratio of this geometric sequence?

      An image in a quiz
      It is positive.
      It is negative.
      It is large.
      It is less than 1.
      Correct answer: It is greater than 1.

      Q5.
      Which of the below could be the ratio of this geometric sequence?

      An image in a quiz
      $$-4$$
      Correct answer: $$1\over4$$
      Correct answer: $$0.4$$
      $$2.5$$
      $$5\over4$$

      Q6.
      You can draw a line through the points of this geometric sequence because it is modelling data that is ...

      An image in a quiz
      constant
      Correct answer: continuous
      discrete
      rapidly increasing
      unknown

      To help you plan your 9 maths lesson on: Representing geometric sequences graphically, download all teaching resources for free and adapt to suit your pupils' needs...