In a geometric sequence, each term after the first is found by multiplying the previous term by a fixed, non-zero number called the common ratio. In your case, the first term a1 is 3, and the common ratio r is -1.
The general formula for the n-th term of a geometric sequence can be expressed as:
an = a1 * r(n-1)
Substituting the known values into this formula, we have:
an = 3 * (-1)(n-1)
Next, we need to determine the domain for n. In general, the index n in a geometric sequence is considered to be a positive integer, which represents the position of the term in the sequence. Therefore, the values of n can be:
- n = 1 (first term)
- n = 2 (second term)
- n = 3 (third term)
- … and so on.
As a result, the domain of n is all positive integers:
Domain of n: n ∈ {1, 2, 3, …} (n is a positive integer)
In conclusion, n must be a positive integer (1, 2, 3, etc.) for the purpose of defining the terms in this specific geometric sequence.