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Math Help - Algerbraic expressions

  1. #1
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    Algerbraic expressions

    I would be every so grateful if you help me with these expressions

    I have 2 create a expression for these 2 sequences

    9 ,15, 25 ,39 ,57 ,


    and


    5, 16, 33, 56, 85,


    like using the nth term
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  2. #2
    MHF Contributor

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    Have you already understood how these sequences work? Like, what is the next term?
    If not, look at the differences between consecutive terms. As you'll see, you can find a simple formula for these differences, and then infer a formula for the initial sequence.

    Of course, there is more than one sequence beginning with the few terms you give, so the question is, in plain rigour, pointless, but the strategy underlined in the above paragraph provides the "simplest" sequence (simplest to define).
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  3. #3
    MHF Contributor

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    It may even not be the simplest... Depending on what you call simple.

    There is a famous website on interesting sequences, called "the encyclopedia of integer sequences". Given your first terms, it returned this sequence. It is the sequence of coefficients of the power series expansion of \frac{1}{-1+x+2x^4} at 0, without the first few terms... The next term would be 87, instead of 79 with the idea of my last post. Of course, your teacher does not expect this answer.

    For the second sequence, the website gives the same sequence as mine, along with a "visual" interpretation.
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