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      Fibonacci and alternating sequences

      Lesson details

      Learning outcome

      I can identify the features of Fibonacci and alternating sequences.

      Key learning points

      1. The next term in the Fibonacci sequence is the sum of the previous two terms.
      2. The Fibonacci sequence can be represented graphically.
      3. An alternating sequence alternates between positive and negative terms.

      Keywords

      • Fibonacci - A Fibonacci sequence is a sequence where each term is the sum of the two previous terms.

      • Alternating - An alternating sequence is a sequence where consecutive terms change sign.

      Common misconception

      Alternating sequences may cause difficulty if negative number skills are not secure.

      A review of negative numbers would be useful. Prior lessons can be used for this review if required.

      Teacher tip

      If possible, ask pupils to investigate the number of petals on various flowers. Is the number of petals one of the terms in the Fibonacci sequence?

      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 could be the first 5 terms in an arithmetic (linear) sequence?

      1, 3, 6, 10, 15, ...
      1, 3, 9, 27, 81, ...
      1, 3, 4, 7, 11, ...
      Correct answer: 1, 3, 5, 7, 9, ...

      Q2.
      Which of these could be the first 5 terms in a geometric sequence?

      1, 3, 6, 10, 15, ...
      Correct answer: 1, 3, 9, 27, 81, ...
      1, 3, 4, 7, 11, ...
      1, 3, 5, 7, 9, ...

      Q3.
      State the $$10^\text {th}$$ term in the sequence with $$n^\text{th}$$ term rule $$3n +1$$

      Correct Answer: 31

      Q4.
      Which sequence could be 'two more than the square numbers'?

      1, 3, 6, 10, ...
      3, 6, 9, 12, ...
      Correct answer: 3, 6, 11, 18, ...
      6, 11, 18, 28, ...
      6, 11, 16, 21, ...

      Q5.
      If a geometric sequence starts 4, 8, 16, 32, ... what is the common ratio (multiplier)?

      $$1\over 2$$
      1
      Correct answer: 2
      4

      Q6.
      If a geometric sequence starts 8, -12, 18, -27, ... what is the common ratio (multiplier)?

      -2
      Correct answer: -1.5
      -1
      0.5

      6 Questions

      Q1.
      A sequence where consecutive terms change sign is called __________

      Correct answer: an alternating sequence.
      an arithmetic sequence.
      a Fibonacci sequence.
      a geometric sequence.
      a quadratic sequence.

      Q2.
      Match the types of sequence to an example of a possible first 5 terms.

      Correct Answer:Alternating,2, -4, 6, -8, 10, ...

      2, -4, 6, -8, 10, ...

      Correct Answer:Arithmetic,2, 4, 6, 8, 10, ...

      2, 4, 6, 8, 10, ...

      Correct Answer:Fibonacci,2, 4, 6, 10, 16, ...

      2, 4, 6, 10, 16, ...

      Correct Answer:Geometric,2, 4, 8, 16, 32, ...

      2, 4, 8, 16, 32, ...

      Q3.
      Here are the first 7 terms in the Fibonacci sequence: 1, 2, 3, 5, 8, 13, 21, ... What is the next term?

      Correct Answer: 34

      Q4.
      Here is a Fibonacci sequence. What is the missing first term?: , 6, 11, 17, 28, ...

      Correct Answer: 5

      Q5.
      Here is a Fibonacci sequence. What is the missing term?: 4, ___, 2, 0, 2, ...

      Correct answer: -2
      -1
      0
      2
      6

      Q6.
      If the first term in a Fibonacci sequence is 12 and the fourth term is 28, what is the second term?

      Correct Answer: 8

      To help you plan your 11 maths lesson on: Fibonacci and alternating sequences, download all teaching resources for free and adapt to suit your pupils' needs...