General term of a sequence

  • Thread starter grupah
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  • #1
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Dear Forum,

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

Best wishes
 

Answers and Replies

  • #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)
 
  • #3
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What is your definition of sequence, exactly?
 
  • #4
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Is it possible to represent all the terms of the sequence by the general term?
 
  • #5
tiny-tim
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i don't understand :confused:

can you give an example of what you're thinking of?​
 
  • #6
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Consider the sequence of prime numbers: {2,3,5,7,dots}
Does it have a general term?
 
  • #7
tiny-tim
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Consider the sequence of prime numbers: {2,3,5,7,dots}
Does it have a general term?

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