To solve this problem, we need to identify the common ratio in a geometric sequence where each term is the previous term divided by 2, starting with an initial term of 12.
1. Let's denote the first term of the sequence as [tex]\(a_1\)[/tex]:
[tex]\[
a_1 = 12
\][/tex]
2. In a geometric sequence, every term after the first is found by multiplying the previous term by a constant called the common ratio, which we'll denote as [tex]\(r\)[/tex].
3. According to the problem, each term is obtained by dividing the previous term by 2. This equivalently means multiplying by [tex]\( \frac{1}{2} \)[/tex] because dividing by 2 is the same as multiplying by [tex]\( \frac{1}{2} \)[/tex].
Therefore:
[tex]\[
a_2 = a_1 \times \frac{1}{2} = 12 \times \frac{1}{2} = 6
\][/tex]
[tex]\[
a_3 = a_2 \times \frac{1}{2} = 6 \times \frac{1}{2} = 3
\][/tex]
And so forth.
4. Generalizing this, the term [tex]\(a_n\)[/tex] would be given by:
[tex]\[
a_n = a_1 \times \left( \frac{1}{2} \right)^{n-1}
\][/tex]
From this, it is clear that the common ratio [tex]\( r \)[/tex] in the explicit formula for this geometric sequence is [tex]\( \frac{1}{2} \)[/tex].
So, the value that can be used as the common ratio in an explicit formula representing the sequence is:
[tex]\(
\boxed{\frac{1}{2}}
\)[/tex]
