Explain why the set of natural numbers is used in the genera

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

Solution

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.)