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Explain why the set of natural numbers is used in the general term of a sequence

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sasuke24 | Student, Undergraduate | (Level 2) Honors

Posted January 13, 2013 at 7:53 PM via web

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Explain why the set of natural numbers is used in the general term of a sequence

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embizze | High School Teacher | (Level 1) Educator Emeritus

Posted January 13, 2013 at 8:07 PM (Answer #1)

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A sequence is an ordered list of numbers. There is a first term, a second term, etc... It makes no sense to ask about the 1/2th term.

Thus we speak of the general term, or nth term, where `n in NN` (n is a natural number.) The formula for the nth term, if there is one, must involve n so that terms are differentiated. (Not all sequences have a formula for the nth term, or are able to be described by a general term. For instance, the sequence of primes has no formula for the nth term. Nor does the sequence of the digits in the decimal expansion for pi.)

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