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Sequences (Nth Term)

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

    Show answer
    (a) \(11,\ 14,\ 17\)
    (b) \(9\)
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  2. Either paper 1 mark

    Here are the first four terms of a sequence.

    \(10\), \(14\), \(20\), \(28\)

    Write down the next term of this sequence.

    Show answer
    \(38\)
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  3. Either paper 4 marks
    Here is a table of values.
    \(x\)4   81012
    \(y\)      1173
    The \(x\)-values in the table make a linear sequence. The \(y\)-values in the table make a different linear sequence.
    (a)

    Complete the table.

    (b)

    The points \((8, 11)\), \((10, 7)\) and \((12, 3)\) are plotted and joined by a straight line.

    xy24681012141234567891011120

    Use the graph to write down the value of \(y\) when \(x = 9\).

    Show answer
    (a) \(x = 6\), \(y = 19\) and \(y = 15\)
    (b) \(9\)
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  4. Either paper 3 marks

    Here are the first three patterns in a sequence. Each pattern is drawn on squared paper and some of its squares are marked with a dot.

    Pattern 1

    xy

    Pattern 2

    xy

    Pattern 3

    xy
    (a)

    Draw pattern 4 on the grid. Mark its squares with dots.

    xy
    (b)

    How many squares in pattern 7 would be marked with a dot?

    Show answer
    (a) Pattern 4 with 4 dotted squares on each of the 3 arms and the square where the bar meets the stem, 13 dotted squares in all
    (b) \(22\)
    (a)xy
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  5. Either paper 2 marks

    A pattern of square tiles grows in the same way each time.

    Pattern 1 uses \(9\) tiles, pattern 2 uses \(16\) tiles, pattern 3 uses \(23\) tiles and pattern 4 uses \(30\) tiles.

    Find an expression, in terms of \(n\), for the number of tiles in pattern \(n\).

    Show answer
    \(7n + 2\)
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  6. Either paper 2 marks

    The \(n\)th term of a sequence is \(8n - 1\)

    One term of the sequence is equal to \(295\).

    Work out the position of that term in the sequence.

    Show answer
    \(37\)
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  7. Either paper 4 marks

    A term-to-term rule is shown in a flow diagram. Each term goes in and the next term of the sequence comes out.

    (a)
    term→+ 1→× 2→next term
    The 1st term of the sequence is \(8\). Find the 3rd term.
    (b) A different sequence has this rule.
    term→× 4→+ 12→next term
    The 2nd term of this sequence is \(40\). Find the 1st term.
    Show answer
    (a) \(38\)
    (b) \(7\)
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  8. Either paper 3 marks
    The table shows the first five terms of four sequences. Below it are six descriptions.
    SequenceFirst five termsDescription letter
    110, 15, 21, 28, 36 
    225, 36, 49, 64, 81 
    34, 5, 9, 14, 23F
    424, 20, 16, 12, 8 
    LetterDescription
    ASquare numbers
    BTriangular numbers
    CArithmetic, increasing (add the same number each time)
    DArithmetic, decreasing (subtract the same number each time)
    EGeometric (multiply by the same number each time)
    FFibonacci-type (each term is the sum of the two before it)
    Match each sequence to its description. Sequence 3 has been done for you: it is description F.
    Show answer
    Sequence 1: B; sequence 2: A; sequence 4: D
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  9. Either paper 3 marks
    Here are the first three patterns in a sequence made up of small squares.
    Pattern 1Pattern 2Pattern 3
    ■■ ■■ ■ ■
    ■ ■■ ■ ■
    ■ ■ ■
    and 49 extra squaresand 49 extra squaresand 49 extra squares
    The number of small squares in pattern \(n\) is \(n^2 + 49\)
    (a)

    Work out the number of small squares in pattern 5.

    (b)

    Work out the least value of \(n\) for which the number of small squares is greater than 110.

    Show answer
    (a) \(74\)
    (b) \(8\)
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  10. Either paper 4 marks

    Here are the first four terms of an arithmetic sequence.

    \(22,\ 17,\ 12,\ 7\)

    (a)

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

    (b)

    Work out the 40th term of this sequence.

    Show answer
    (a) \(-5n + 27\)
    (b) \(-173\)
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discia.org Sequences (Nth Term) · sheet 1
Answers Sequences (Nth Term) · sheet 1
  1. (a) \(11,\ 14,\ 17\)
    (b) \(9\)
  2. \(38\)
  3. (a) \(x = 6\), \(y = 19\) and \(y = 15\)
    (b) \(9\)
  4. (a) Pattern 4 with 4 dotted squares on each of the 3 arms and the square where the bar meets the stem, 13 dotted squares in all
    (b) \(22\)
    (a)xy
  5. \(7n + 2\)
  6. \(37\)
  7. (a) \(38\)
    (b) \(7\)
  8. Sequence 1: B; sequence 2: A; sequence 4: D
  9. (a) \(74\)
    (b) \(8\)
  10. (a) \(-5n + 27\)
    (b) \(-173\)
discia.org Sequences (Nth Term) · sheet 1