# General term of a sequence

Dear Forum,

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

Best wishes

tiny-tim
Homework Helper
hi grupah! 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 (if you mean is there a straightforward formula for an, the answer is not necessarily, it depends how the sequence is defined)

What is your definition of sequence, exactly?

Is it possible to represent all the terms of the sequence by the general term?

tiny-tim
Homework Helper
i don't understand can you give an example of what you're thinking of?​

Consider the sequence of prime numbers: {2,3,5,7,dots}
Does it have a general term?

tiny-tim
Homework Helper
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")

So, what is the mathematical definition of the general term, a kind of explanation?

tiny-tim
it uniquely defines the number, and that's all maths requires 