To find the equation for the \( n \)th term of an arithmetic sequence, we need to use the following formula for the \( n \)th term \( a_n \):
[tex]\[ a_n = a_1 + (n-1)d \][/tex]
Where:
- \( a_1 \) is the first term of the sequence.
- \( d \) is the common difference between the terms.
- \( n \) is the term number.
Given:
- The first term \( a_1 = 28 \)
- The common difference \( d = -6 \)
Let's substitute these values into the formula:
[tex]\[ a_n = 28 + (n-1)(-6) \][/tex]
Next, simplify the expression inside the parentheses:
[tex]\[ a_n = 28 + (-6)(n-1) \][/tex]
Now distribute the \(-6\):
[tex]\[ a_n = 28 - 6(n-1) \][/tex]
Thus, the equation for the \( n \)th term of the arithmetic sequence is:
[tex]\[ a_n = 28 - 6(n-1) \][/tex]
This matches the fourth option provided in the multiple-choice question. Therefore, the answer is:
[tex]\[ \boxed{a_n = 28 - 6(n-1)} \][/tex]
And hence, the correct option is the fourth one.
