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What is a general term and how is it different than a function?

  1. May 30, 2012 #1
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution




    I don't know how to use the above template considering I don't actually have a specific question from my homework, but I do have a question that I need answered to complete my homework.




    Anyway, my book asks me to write a function that would correspond to a sequence, and then later asks me to write a general term for the nth term of that same sequence.

    Would these be the same answer? I wrote them down as the same answer just with n instead of x for the general term question. They also asked me for a recursive formula for the sequence.


    Can a general term be a recursive formula or a non recursive formula?




    Thanks in advance. I just really don't understand what a general term is. Is it possible that they want the same answer for the general term and recursive formula, or function?



    My problem is really that after writing a function, and a recursive formula for a sequence, I can't think of any other way to write a formula differently that could be considered a general term. I don't know what a general term is in the first place though.
     
    Last edited: May 30, 2012
  2. jcsd
  3. May 30, 2012 #2

    HallsofIvy

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    So your question is about the "general term of a sequence". If a sequence is, for example, 1, 1/2, 1/3, 1/4, 1/5, ... so each term is of the 1/n for some n. The "general term" is "1/n".

    No, a "term" is not a "formula" but a formula might involve one or more terms. For example, a recursion formula typically says that a given term is some function of the previous terms. For example (although its a bit of a stretch), we can write [itex]a_{n+1}= 1/(n+1)[/itex] as [itex](1/n)- 1/(n(n+1))[/itex] so we can write [itex]a_{n+1}= a_n- 1/(n(n+1))[/itex], a recurrance formula.

    Perhaps it would help if you gave a specific example. What "function" are you talking about?
     
  4. May 30, 2012 #3
    Okay, so this specific question has
    x = 1, 2, 3, 4
    f(x) = 0, 3, 8, 15

    for this sequence's function I wrote x^(2) - 1.

    Is the general term the same answer but with an n instead of x?

    thanks
     
  5. Jun 1, 2012 #4
    Yup, you don't really need to change the ##x## to an ##n##, actually. It is just a convention. It is like:

    $$a_n=n^2-1$$
     
  6. Jun 1, 2012 #5
    Thanks a lot. It's very helpful to get an answer to this.
     
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