# General term of a sequence

1. Dec 27, 2013

### grupah

Dear Forum,

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

Best wishes

2. Dec 27, 2013

### tiny-tim

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)

3. Dec 27, 2013

### Millennial

What is your definition of sequence, exactly?

4. Dec 27, 2013

### grupah

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

5. Dec 27, 2013

### tiny-tim

i don't understand

can you give an example of what you're thinking of?​

6. Dec 27, 2013

### grupah

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

7. Dec 27, 2013

### tiny-tim

no, there's no formula (other than "an is the nth prime")

8. Dec 27, 2013

### grupah

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

9. Dec 27, 2013

### tiny-tim

"the nth prime" is a mathematical definition!

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