AQA · Mathematics · 8300

GCSE Maths: Sequences: Fibonacci

Algebra · AQA GCSE Maths (8300). Cards are generated from the Corbettmaths practice questions for Sequences: Fibonacci (Corbettmaths Video 287), and every card links back to the exact page it came from. Practice tests are drawn from this deck’s own cards. Source material © Corbettmaths — used with attribution.

9 flashcards · Free to study · No account needed

Sign in and GCSE Zone remembers what you know: cards you have nailed drop out of your study until they are due again.

Study this deck

Preparing your cards…

All questions and answers

Read through the full deck, or practise recalling each answer above.

  1. How is each term in a Fibonacci sequence generated?

    Show answer

    By adding the two previous terms together.

  2. Can a Fibonacci sequence contain negative numbers?

    Show answer

    Yes. For example, starting with 2, −7 gives −5, then −12, and so on.

  3. Given a Fibonacci sequence with first term 1 and fourth term 27, what is the second term?

    Show answer

    13. If the terms are 1, a, b, 27, then 1 + a = b and a + b = 27. Substituting: a + (1 + a) = 27 → 2a = 26 → a = 13.

  4. In a Fibonacci sequence where the fifth term is 0 and the sixth term is 4, what is the first term?

    Show answer

    −12. Working backward: term₄ = 4, term₃ = −4, term₂ = 8, term₁ = −12.

  5. If the first three terms of a Fibonacci sequence are x, 3x, and 4x, what is the 5th term?

    Show answer

    11x. Term₄ = 3x + 4x = 7x; Term₅ = 4x + 7x = 11x.

  6. If the first two terms of a Fibonacci sequence are y and 6, what is the 4th term?

    Show answer

    y + 12. Term₃ = y + 6; Term₄ = 6 + (y + 6) = y + 12.

  7. If the first two terms of a Fibonacci sequence are x and y, what is the fourth term?

    Show answer

    x + 2y. Term₃ = x + y; Term₄ = y + (x + y) = x + 2y.

  8. If the first term of a Fibonacci sequence is x and the third term is 2y, what is the fifth term?

    Show answer

    6y − x. Term₂ = 2y − x; Term₄ = 4y − x; Term₅ = 2y + (4y − x) = 6y − x.

  9. In a Fibonacci sequence 3x, 4x, 7x, ..., if the difference between the 6th and 3rd terms is 132, what is the value of x?

    Show answer

    x = 6. Continuing: 11x, 18x, 29x. So 29x − 7x = 22x = 132 → x = 6.

Want to create your own cards? Create a free account. AI generation uses credits.