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

Solution:

In the geometric sequence a\(_1\) = a = 3

Common ratio r = - 1

We shall determine the general term of geometric sequence

a\(_n\) = ar^{n - 1}

Substituting the values

a\(_n\) = 3 × (-1)^{n - 1}

This can be written as a function

f (n) = 3 (-1)^{n - 1}

Take f (1) = 3 for n = 1

Geometric series begins from n = 1

Domain n ≥ 1

Therefore, the domain for n is all integers where n ≥ 1.

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

Summary:

Given the geometric sequence where a1 = 3 and the common ratio is −1, the domain for n is all integers where n ≥ 1.