To determine the next term in the sequence: [tex]\(16, 11, 8.5, 7.25, ?\)[/tex],
we first observe the pattern of differences between consecutive terms:
1. The difference between the first and second terms: [tex]\(16 - 11 = 5\)[/tex]
2. The difference between the second and third terms: [tex]\(11 - 8.5 = 2.5\)[/tex]
3. The difference between the third and fourth terms: [tex]\(8.5 - 7.25 = 1.25\)[/tex]
Next, notice that the differences themselves follow a pattern; each difference is half of the previous one:
- [tex]\(5\)[/tex]
- [tex]\(\frac{5}{2} = 2.5\)[/tex]
- [tex]\(\frac{2.5}{2} = 1.25\)[/tex]
By continuing this pattern, the next difference should be:
[tex]\[ \frac{1.25}{2} = 0.625 \][/tex]
Now, subtract this difference from the fourth term to find the next term:
[tex]\[ 7.25 - 0.625 = 6.625 \][/tex]
Therefore, the next term in the sequence is:
[tex]\(
\boxed{6.625}
\)[/tex]
Thus, the answer is 6.625.
