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Sequences and series help / recurrence relation

  1. Oct 28, 2008 #1
    1. The problem statement, all variables and given/known data

    A sequence of terms [tex] U_{k} [/tex] is defined by [tex] K \geq [/tex] by the recurrence relation [tex] U_{k+2} = U_{k+1} - pU_{k} [/tex] where P is a constant Given that [tex] U_{1} =2 [/tex] and [tex] U_{2} = 4 [/tex]

    a) find an expression in terms of p for [tex] U_{3} [/tex]

    b) hence find an expression in terms of p for [tex] U_{4} [/tex]

    given also that [tex] U_{4} [/tex] is twice the value of [tex] U_{3} [/tex]
    c) find the value of p

    3. The attempt at a solution

    for question a i just subsititue k=1 and i get [tex] U_{3} = 4 - 2p [/tex] and for B i substituted k=2 and the expression i got is [tex] U_{4} = 4-6p [/tex]

    what i am really stuck on is how to work out the value of 'p' ????

    can anyone please show me ?

    thanks!
     
  2. jcsd
  3. Oct 28, 2008 #2

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    Excellent! You have done exactly what you should have done. Now use that last condition, U4 is twice the value of U3 or U4= 3U3 with the U3 and U4 you have and solve for p.
     
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