To determine the explicit rule for the arithmetic sequence, we need to identify the first term and the common difference of the sequence. The explicit rule can then be written in the general form:
[tex]\[ a_n = a_1 + (n - 1)d \][/tex]
where [tex]\(a_1\)[/tex] is the first term and [tex]\(d\)[/tex] is the common difference.
Given the answer, we can extract the relevant details as follows:
1. First Term ([tex]\(a_1\)[/tex]):
The first term of the sequence is [tex]\( \frac{3}{2} \)[/tex].
2. Common Difference ([tex]\(d\)[/tex]):
The common difference is [tex]\( \frac{1}{6} \)[/tex].
Substituting these values into the general form of the explicit rule for an arithmetic sequence, we get:
[tex]\[ a_n = \frac{3}{2} + (n - 1) \cdot \frac{1}{6} \][/tex]
Thus, the explicit rule for the arithmetic sequence is:
[tex]\[ a_n = \frac{3}{2} + (n - 1) \cdot \frac{1}{6} \][/tex]
Therefore, the correct answer is:
[tex]\[ a_n = \frac{3}{2} + (n - 1) \cdot \frac{1}{6} \][/tex]
