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Math Help - recurrence relation issues

  1. #1
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    recurrence relation issues

    The solution to the recurrence relation a_n = a_n-1 + 3 with initial condition a0 = 2

    The answer that I got was

    an = 3 + lg 2n

    I know that the answer will be similar to this in form I am just not feeling confident in the answer I came up with.

    Thanks for taking a look.

    pwr
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  2. #2
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    Quote Originally Posted by pwr_hngry View Post
    The solution to the recurrence relation a_n = a_n-1 + 3 with initial condition a0 = 2

    The answer that I got was

    an = 3 + lg 2n

    I know that the answer will be similar to this in form I am just not feeling confident in the answer I came up with.

    Thanks for taking a look.

    pwr
    Well,
    a_0 = 2
    and your formula gives:
    a_0 = 3 + lg(2 \cdot 0) \to \infty
    (I presume "lg" is a logarithm function to some base?)

    Let's take a look at the sequence.
    a_0 = 2
    a_1 = a_0 + 3 = 2 + 3 = 5
    a_2 = a_1 + 3 = 5 + 3 = 8
    a_3 = a_2 + 3 = 8 + 3 = 11
    etc.

    So it looks like:
    a_n = a_0 + 3n = 3n + 2

    -Dan
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