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

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.