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

The Nth Term of a Quadratic Sequence

discia.org 10 questions · 27 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 3 marks

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

    \(n^2 +n + 3\)

    One term of the sequence is equal to \(75\).

    Find the position of that term in the sequence.

    Show answer
    \(n = 8\)
    Another like this
  6. Either paper 3 marks

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

    \(n^2 -n - 7\)

    Work out the first term of the sequence that is greater than \(52\).

    Show answer
    \(65\)
    Another like this
  7. Either paper 3 marks

    A quadratic sequence begins

    \(8,\ 19,\ 36,\ 59,\ \dots\)

    Is 391 a term of this sequence?

    You must explain your answer.

    Show answer
    No — the 11th term is 388 and the 12th term is 459, so 391 is not a term of the sequence.
    Another like this
  8. Either paper 3 marks

    Here are the first four terms of a quadratic sequence.

    \(12,\ 26,\ 44,\ 66\)

    (a)

    Work out the next two terms of the sequence.

    (b)

    State the second difference of the sequence.

    Show answer
    (a) \(92\) and \(122\)
    (b) \(4\)
    Another like this
  9. Either paper 2 marks

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

    \(n^2 + 2n + 15\)

    Write down the first three terms of the sequence.

    Show answer
    \(18,\ 23,\ 30\)
    Another like this
  10. Either paper 3 marks

    Here are five terms of a quadratic sequence. The third term is missing.

    \(-2,\ 10,\ ?,\ 52,\ 82\)

    Work out the missing term.

    Show answer
    \(28\)
    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. \(n = 8\)
  6. \(65\)
  7. No — the 11th term is 388 and the 12th term is 459, so 391 is not a term of the sequence.
  8. (a) \(92\) and \(122\)
    (b) \(4\)
  9. \(18,\ 23,\ 30\)
  10. \(28\)
discia.org The Nth Term of a Quadratic Sequence · sheet 1