Question

Given the geometric sequence where a1=3 and the common ratio is -1, what is the domain for n?

Answer 1

Answer:

  natural numbers

Step-by-step explanation:

As it is for any sequence, the domain of term numbers (n) is the positive integers, the natural numbers.

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When the common ratio is positive, the expression for the n-th term can be evaluated for non-integer values of n. In the context of "term number n", that makes no sense, but you can do it.

When the common ratio is negative, you can also evaluate the expression for the n-th term for non-integer values of n. In such cases, you get a complex number result. That, too, makes no sense in the context of a sequence, but you can do it.

In general, the domain of any "n' that represents something being counted, the domain of n will be the counting numbers.