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General term of a sequence

  1. Dec 27, 2013 #1
    Dear Forum,

    Does every sequence have a general term? What is the definition of the general term of a sequence?

    Best wishes
     
  2. jcsd
  3. Dec 27, 2013 #2

    tiny-tim

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    hi grupah! :smile:

    a sequence is a function whose domain is the natural numbers (or a subset of them)

    so we can write it as {an}nεN,

    and the general term of the sequence is an :wink:

    (if you mean is there a straightforward formula for an, the answer is not necessarily, it depends how the sequence is defined)
     
  4. Dec 27, 2013 #3
    What is your definition of sequence, exactly?
     
  5. Dec 27, 2013 #4
    Is it possible to represent all the terms of the sequence by the general term?
     
  6. Dec 27, 2013 #5

    tiny-tim

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    i don't understand :confused:

    can you give an example of what you're thinking of?​
     
  7. Dec 27, 2013 #6
    Consider the sequence of prime numbers: {2,3,5,7,dots}
    Does it have a general term?
     
  8. Dec 27, 2013 #7

    tiny-tim

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    no, there's no formula (other than "an is the nth prime")
     
  9. Dec 27, 2013 #8
    So, what is the mathematical definition of the general term, a kind of explanation?
     
  10. Dec 27, 2013 #9

    tiny-tim

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    "the nth prime" is a mathematical definition!

    it uniquely defines the number, and that's all maths requires :smile:
     
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