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Math Help - Recurrence Relation

  1. #1
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    Recurrence Relation

    Solve the given recurrence relation with for the initial conditions given.
    a_n = 7a_(n-1) - 10a_(n-2)
    a_0 = 5
    a_1 = 16

    I am missing something and cannot come up with the answer here.

    Pwr
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  2. #2
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    Hello, pwr_hngry!

    Solve the given recurrence relation with for the initial conditions given.
    a
    n .= .7an-1 - 10an-2, .a0 = 5, .a1 = 16
    The characteristic equation is: .r - 7r + 10 .= .0

    . . which factors: .(r - 2)(r - 5) .= .0

    . . and has roots: .r .= .2, 5

    So we have: .a
    n .= .b2^n + c5^n


    From a
    0 = 5, we have: .b2^0 + c5^0 .= .5 . . . . b + c .= .5

    From a
    1 = 16, we have: .b2^1 + c5^1 .= .16 . . . . 2b + 5c .= .16

    Solve the system of equations and get: .b = 3, .c = 2


    Therefore: .a
    n .= .32^n + 25^n

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