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Math Help - recurrence relation

  1. #1
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    recurrence relation

    Can anyone tell me if this is correct for this relation:

    6.1 In the following sequences determine s5 if s0, s1, ... sn, ... is a sequence satisfying the given recurrence relation and initial condition.
    b. sn = -sn-1 - n2 for n >= 1, s0 = 2
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  2. #2
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    Sorry forgot to put in the answers. Here is the answers I got:

    s0 = 2
    s1 = -1
    s2 = 5
    s3 = 4
    s4 = 12
    s5 = 13
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  3. #3
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    Quote Originally Posted by papa_chango123 View Post
    Sorry forgot to put in the answers. Here is the answers I got:

    s0 = 2
    s1 = -1
    s2 = 5
    s3 = 4
    s4 = 12
    s5 = 13
    No,
    s1=-s0-1^2=-2-1=-3
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  4. #4
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    Hello, papa_chango123!

    What is n2?
    Is that your way of writing n^2 ?


    6.1) In the following sequences determine s_5
    if s_n is a sequence satisfying the given recurrence relation and initial condition.
    b)\;s_n \:= \:-s_{n-1}- n^2 . for n \geq 1,\;s_o = 2

    Am I reading it correctly?

    It says: . \underbrace{s_n}_{\text{the nth term}} \;\underbrace{=}_{\text{is}}\;\underbrace{-s_{n-1}}_{\text{neg.of preceding term}} - \underbrace{n^2}_{\text{minus n-squared}}

    So s_1 is the negative of s_o, minus 1^2.
    . . s_1\:=\:-2 - 1^2\:=\:-3

    And s_2 is the negative of s_1, minus 2^2.
    . . s_2\:=\:-(-3) - 2^2 \:=\:-1

    Then s_3 is the negative of s_2, minus 3^2.
    . . s_3\:=\:-(-1) - 3^2 \:=\:-8

    Hence s_4 is the negative of s_3. minus 4^2.
    . . s_4\:=\:-(-8) - 4^2\:=\:-8

    Therefore: s_5 is the negative of s_4, minus 5^2.
    . . s_5\:=\:-(-8) - 5^2\:=\:\boxed{-17}

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  5. #5
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    Yes thanks that is the answer I got.
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