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

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- Thread starter grupah
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- #1

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

Best wishes

- #2

tiny-tim

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

so we can write it as {a

and the general term of the sequence is a

(if you mean is there a straightforward formula for a

- #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

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

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Consider the sequence of prime numbers: {2,3,5,7,dots}

Does it have a general term?

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 "a

- #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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it

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