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Math Help - arithmetic progression

  1. #1
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    arithmetic progression

    I have an arithmetic progression a1, a2, a3,a4,a5...Now, I have:a1=1a2=2a(x)=5a(x-2)+3a(x-1)for x=3,4,5,6,7...How can I check, that there isn't a(n) [for n>2 or n=2)] which divided a(n+2)*a(n+1)
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  2. #2
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    Hello, Helloworld!

    If no one is responding, it's because they can't read your question . . .


    I have an arithmetic progression a1, a2, a3,a4,a5...Now, I have:a1=1a2=2a(x)=5a(x-2)+3a(x-1)for x=3,4,5,6,7...How can I check, that there isn't a(n) [for n>2 or n=2)] which divided a(n+2)*a(n+1)

    Without spaces or commas, it's (almost) impossible to read.
    Luckily, I'm a mathematical archeologist, so I can piece together a statement
    . . from strange-looking fragments.


    Here's what the heiroglyphics say . . .

    We have an arithmetic sequence: . a_1,\,a_2,\,a_3,\,a_4,\,\cdots

    We are given: . a_1 = 1,\;a_2 = 2,\;\;a_n\:=\:3a_{n-1} + 5a_{n-2}

    . . First term is 1; the second term is 2.
    . . Every successive term is 3 times the preceding term plus 5 times the second preceding term.

    We are to prove that a_n does not divide (a_{n+1})(a_{n+2})

    . . A term does not divide the product of the next two terms.

    Anyone care to give it a try?

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