To determine the correct formula for finding the [tex]\(n\)[/tex]th term of a geometric sequence, we need to follow these steps:
1. Identify the first term ([tex]\(a_1\)[/tex]): The first term of the sequence is given as 8.
2. Identify the common ratio ([tex]\(r\)[/tex]): The common ratio of this sequence is given as -3.
3. Recall the general formula for a geometric sequence: The general formula for the [tex]\(n\)[/tex]th term of a geometric sequence is given by:
[tex]\[
a_n = a_1 \cdot r^{n-1}
\][/tex]
Now, substitute the given values into the general formula:
4. Substitute [tex]\(a_1 = 8\)[/tex] and [tex]\(r = -3\)[/tex] into the formula:
[tex]\[
a_n = 8 \cdot (-3)^{n-1}
\][/tex]
By substituting the specific values for the first term and the common ratio into the general formula for the [tex]\(n\)[/tex]th term of a geometric sequence, we get:
[tex]\[
a_n = 8 \cdot (-3)^{n-1}
\][/tex]
Thus, the correct formula to find the [tex]\(n\)[/tex]th term of this geometric sequence is:
[tex]\[
\boxed{a_n = 8 \cdot (-3)^{n-1}}
\][/tex]
