Discia GCSE Maths › Algebra › Sequences (Nth Term)

Sequences (Nth Term) worksheet

10 GCSE practice questions with answers, free to print. Every sheet is generated, so you can make a fresh one whenever you need it.

10 questions 30 marks Sheet 1
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  1. 4 marks

    The \(n\)th term of a sequence is \(3n + 8\).

    (a)

    Write down the first three terms of the sequence.

    (b)

    One term of this sequence is equal to 35.

    Work out the value of \(n\) for that term.

  2. 2 marks

    A sequence begins

    \(1,\ 7,\ 13,\ 19,\ \dots\)

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

  3. 2 marks

    The \(n\)th term of a sequence is \(9n + 4\)

    One term of the sequence is equal to \(364\).

    Find the position of that term in the sequence.

  4. 4 marks

    Here are the first four terms of an arithmetic sequence.

    \(60,\ 57,\ 54,\ 51\)

    (a)

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

    (b)

    Work out the 100th term of this sequence.

  5. 3 marks

    Here are the first four terms of an arithmetic sequence.

    \({a1},\ {t2},\ {t3},\ {t4}\)

    Is {target} a term of this sequence?

    You must explain your answer.

  6. 3 marks

    In an arithmetic sequence the 2nd term is \(16\) and the 8th term is \(46\).

    Work out an expression for the \(n\)th term of the sequence.

  7. 4 marks

    The \(n\)th term of a sequence is \(5n + 6\).

    (a)

    Write down the first three terms of the sequence.

    (b)

    One term of this sequence is equal to 56.

    Find the value of \(n\) for that term.

  8. 2 marks

    A sequence begins

    \(14,\ 20,\ 26,\ 32,\ \dots\)

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

  9. 2 marks

    The \(n\)th term of a sequence is \(6n + 2\)

    One term of the sequence is equal to \(194\).

    Work out the position of that term in the sequence.

  10. 4 marks

    A sequence begins

    \(37,\ 30,\ 23,\ 16,\ \dots\)

    (a)

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

    (b)

    Work out the 30th term of this sequence.

Answers

  1. (a) \(11,\ 14,\ 17\)
    (b) \(9\)
  2. \(6n - 5\)
  3. \(40\)
  4. (a) \(-3n + 63\)
    (b) \(-237\)
  5. {verdict} — solving \({d}n {b:+} = {target}\) gives \(n = {quo:mixed}\), {whichis} a whole number.
  6. \(5n + 6\)
  7. (a) \(11,\ 16,\ 21\)
    (b) \(10\)
  8. \(6n + 8\)
  9. \(32\)
  10. (a) \(-7n + 44\)
    (b) \(-166\)

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