[discia] GCSE Maths › Algebra › The Nth Term of a Quadratic Sequence

The Nth Term of a Quadratic Sequence

discia.org 10 questions · 30 marks
Name Date
  1. Either paper 3 marks

    Here are the first four terms of a quadratic sequence.

    \(1,\ 18,\ 45,\ 82\)

    (a)

    Work out the next two terms of the sequence.

    (b)

    State the second difference of the sequence.

    Show answer
    (a) \(129\) and \(186\)
    (b) \(10\)
    Another like this
  2. Either paper 2 marks

    The \(n\)th term of a quadratic sequence is

    \(3n^2 + 7n - 9\)

    Write down the first three terms of the sequence.

    Show answer
    \(1,\ 17,\ 39\)
    Another like this
  3. Either paper 3 marks

    Five terms of a quadratic sequence are shown below. One of them is missing.

    \(19,\ 37,\ ?,\ 103,\ 151\)

    Work out the missing term.

    Show answer
    \(65\)
    Another like this
  4. Either paper 2 marks

    Here are the first five terms of each of three sequences.

    A  \(3,\ 18,\ 41,\ 72,\ 111\)

    B  \(3,\ 9,\ 27,\ 81,\ 243\)

    C  \(6,\ 8,\ 10,\ 12,\ 14\)

    Exactly one of them is a quadratic sequence.

    Write down the letter of the quadratic sequence, and explain how you can tell.

    Show answer
    \(A\). Its second differences are all \(8\) — equal to each other and not zero, which is what makes a sequence quadratic.
    Another like this
  5. Either paper Higher3 marks

    The table gives the first five terms of a quadratic sequence.

    Position12345
    Term516335685

    Find an expression, in terms of \(n\), for the \(n\)th term of the sequence.

    Show answer
    \(3n^2 + 2n \)
    Another like this
  6. Either paper Higher5 marks

    A quadratic sequence begins

    \(7,\ 19,\ 35,\ 55,\ 79,\ \dots\)

    (a)

    Find an expression, in terms of \(n\), for the \(n\)th term of the sequence.

    (b)

    Work out the 12th term of the sequence.

    Show answer
    (a) \(2n^2 + 6n - 1\)
    (b) \(359\)
    Another like this
  7. Either paper 3 marks

    The \(n\)th term of a quadratic sequence is

    \(n^2 + 3n - 5\)

    One term of the sequence is equal to \(83\).

    Find the position of that term in the sequence.

    Show answer
    \(n = 8\)
    Another like this
  8. Either paper Higher3 marks

    The \(n\)th term of a quadratic sequence is \(an^2 + bn + c\).

    The second difference of the sequence is \(2\).

    The first term is \(18\) and the second term is \(23\).

    (a)

    Write down the value of \(a\).

    (b)

    Work out the value of \(b\) and the value of \(c\).

    Show answer
    (a) \(a = 1\)
    (b) \(b = 2\) and \(c = 15\)
    Another like this
  9. Either paper 3 marks

    The \(n\)th term of a quadratic sequence is

    \(n^2 + 4n + 9\)

    Work out the first term of the sequence that is greater than \(33\).

    Show answer
    \(41\)
    Another like this
  10. Either paper 3 marks

    A quadratic sequence begins

    \(0,\ 7,\ 18,\ 33,\ \dots\)

    Is 133 a term of this sequence?

    You must explain your answer.

    Show answer
    Yes — the 8th term is 133 and the 9th term is 168, so 133 is a term of the sequence.
    Another like this
discia.org The Nth Term of a Quadratic Sequence · sheet 1
Answers The Nth Term of a Quadratic Sequence · sheet 1
  1. (a) \(129\) and \(186\)
    (b) \(10\)
  2. \(1,\ 17,\ 39\)
  3. \(65\)
  4. \(A\). Its second differences are all \(8\) — equal to each other and not zero, which is what makes a sequence quadratic.
  5. \(3n^2 + 2n \)
  6. (a) \(2n^2 + 6n - 1\)
    (b) \(359\)
  7. \(n = 8\)
  8. (a) \(a = 1\)
    (b) \(b = 2\) and \(c = 15\)
  9. \(41\)
  10. Yes — the 8th term is 133 and the 9th term is 168, so 133 is a term of the sequence.
discia.org The Nth Term of a Quadratic Sequence · sheet 1