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Math Help - Fibonacci sequence

  1. #1
    Junior Member
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    Question Fibonacci sequence

    I have from a previous question these answers:

    Fn+3 = Fn+2 + Fn+1 & Fn = Fn+2 - Fn+1

    I have to use these answers to show that:

    Fn+3 + Fn = 2Fn+2 & Fn+3 - Fn = 2Fn+1 for n = 0, 1, 2,...

    I'm not sure how to do this although I understand that the second set of statements are true.
    Any help would be really appreciated
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by bigroo View Post
    I have from a previous question these answers:

    Fn+3 = Fn+2 + Fn+1 & Fn = Fn+2 - Fn+1

    I have to use these answers to show that:

    Fn+3 + Fn = 2Fn+2 & Fn+3 - Fn = 2Fn+1 for n = 0, 1, 2,...

    I'm not sure how to do this although I understand that the second set of statements are true.
    Any help would be really appreciated
    You want to show that:

    F_{n+3}+F_n=2F_{n+2}

    You begin by using the recurrence for the Fibonacci numbers on F_{n+3}, then group terms if you try that and have further difficulties post what you have done and tell us what difficulties you are having with it.

    CB
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