Let's analyze the given sequence: 12, 6, 3, ...
To find the pattern and determine the next term, we examine the changes between consecutive terms:
- The first term is 12.
- The second term is 6. To get from 12 to 6, we divide by 2: [tex]\( \frac{12}{2} = 6 \)[/tex].
- The third term is 3. To get from 6 to 3, we again divide by 2: [tex]\( \frac{6}{2} = 3 \)[/tex].
Observing this pattern of repeatedly dividing by 2, let's apply the same rule to the third term to find the next term:
- The current term is 3.
- Dividing by 2, we have: [tex]\( \frac{3}{2} = 1.5 \)[/tex].
Therefore, the next term in the sequence is [tex]\(1.5\)[/tex], which can also be written as [tex]\(1 \frac{1}{2}\)[/tex].
So, the next term of the sequence is:
[tex]\[ 1 \frac{1}{2} \][/tex]
