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Sequences and series: Arithmetic · PDF file Sequences and series: Arithmetic series 8.1 Sequences LO: To be able to find the formula for the terms of a sequence . 8, 11, 14, 17, u

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  • Sequences and series:

    Arithmetic series

    8.1 Sequences

    LO: To be able to find the formula for the terms of a sequence

  • 8, 11, 14, 17, …

     u1 = first term

     u2 = second term…

    Term-to-term rule (recurrence relation – give first term in sequence and the

    relationship between successive terms)

    General term / nth term

  • 5, 9, 13, 17, ….

    Term-to-term rule

    (recurrence relation)

    General term / nth term

  • 15, 12, 9, 6, ….

    Term-to-term rule

    (recurrence relation)

    General term / nth term

  • Ignore the signs – Find the nth term.

    (-1)n = -1 when n is odd

    (-1)n = +1 when n is even

    Do the signs of the terms alternate?

    2n(-1)n

    1)1(  n

    ,...8,6,4,2 

    1)1(  n

  • 1)1)(82(  nn

    ,...16,14,12,10 

  • 1)1)(112(  nn

    ,...3,5,7,9 

  • If the numbers go up rapidly and are not

    obviously being multiplied by the same

    number, the nth term could contain a

    square or a cube or a quadratic.

    ,...81,64,27,8,1 

    13 )1(  nn

  • ,...25,16,9,4,1 

    12 )1(  nn

  • ,...8,4,2,1

    12 n

    Look for powers of numbers

  • nth term is given:

    1. Find the first 4 terms

    of the sequence.

    nn x

    2

    1 

    2. Which term in the

    sequence is

    3. Express the

    sequence as a

    recurrence relation

    1024

    1

  • A sequence is defined by a recurrence relation of

    the form

    Given that M1 = 10, M2 = 20, M3 = 24, find the value

    of a and the value of b and hence find M4.

    baMM nn 1

  • Page 133 Exercise 8A

    Questions 1 a, c, e

    2 a, b, c and 6