Let's analyze the arithmetic sequence given: [tex]\(-36,-30,-24,-18,-12\)[/tex].
To determine the formula for the sequence, we will break it down step-by-step:
1. Identify the first term:
[tex]\[
a = -36
\][/tex]
2. Determine the common difference (d):
The common difference [tex]\(d\)[/tex] is calculated by subtracting the first term from the second term:
[tex]\[
d = -30 - (-36) = -30 + 36 = 6
\][/tex]
3. Use the formula for the [tex]\(n\)[/tex]th term of an arithmetic sequence:
The formula for the [tex]\(n\)[/tex]th term of an arithmetic sequence is:
[tex]\[
f(n) = a + (n - 1)d
\][/tex]
4. Substitute the identified values [tex]\(a\)[/tex] and [tex]\(d\)[/tex] into the formula:
[tex]\[
a = -36, \quad d = 6
\][/tex]
[tex]\[
f(n) = -36 + (n - 1) \cdot 6
\][/tex]
5. Simplify the formula:
[tex]\[
f(n) = -36 + 6(n - 1)
\][/tex]
[tex]\[
f(n) = -36 + 6n - 6
\][/tex]
[tex]\[
f(n) = -42 + 6n
\][/tex]
After careful verification, we realize that while this specific form might be correct, the exact formulation from the original problem doesn't require us to simplify completely. Instead, we should match it to the provided options directly after substituting the identified [tex]\(a\)[/tex] and [tex]\(d\)[/tex].
6. Evaluate the provided options to see which matches our derived formula:
[tex]\[
f(n) = -36 + 6(n - 1)
\][/tex]
Checking each option, we find that the correct representation matches this derived formula.
Thus, the correct option representing the formula for the sequence is:
[tex]\[
f(n) = -36 + 6(n - 1)
\][/tex]
So, the correct option is:
[tex]\[
\boxed{1}
\][/tex]
