To determine which sequence shows a pattern where each term is 1.5 times the previous term, let’s analyze each sequence step-by-step.
### Sequence 1:
[tex]\(-4, 6, -9, 13.5, \ldots\)[/tex]
- Check the ratio:
[tex]\[
\frac{6}{-4} = -1.5
\][/tex]
[tex]\[
\frac{-9}{6} = -1.5
\][/tex]
[tex]\[
\frac{13.5}{-9} = -1.5
\][/tex]
The ratio between each consecutive term is [tex]\(-1.5\)[/tex]. Therefore, this is not the correct sequence as we need a ratio of 1.5.
### Sequence 2:
[tex]\(10, 15, 25, 40, \ldots\)[/tex]
- Check the ratio:
[tex]\[
\frac{15}{10} = 1.5
\][/tex]
[tex]\[
\frac{25}{15} \approx 1.67
\][/tex]
The ratio between the second and the third term is not 1.5. Therefore, this is not the correct sequence.
### Sequence 3:
[tex]\(98, 99.5, 101, 102.5, \ldots\)[/tex]
- Check the ratio:
[tex]\[
\frac{99.5}{98} \approx 1.015
\][/tex]
[tex]\[
\frac{101}{99.5} \approx 1.015
\][/tex]
The ratio between consecutive terms is approximately 1.015, not 1.5. Therefore, this is not the correct sequence.
### Sequence 4:
[tex]\(-200, -300, -450, -675, \ldots\)[/tex]
- Check the ratio:
[tex]\[
\frac{-300}{-200} = 1.5
\][/tex]
[tex]\[
\frac{-450}{-300} = 1.5
\][/tex]
[tex]\[
\frac{-675}{-450} = 1.5
\][/tex]
The ratio between each consecutive term is exactly 1.5. Therefore, this is the correct sequence.
Thus, the sequence that shows a pattern where each term is 1.5 times the previous term is:
[tex]\[
-200, -300, -450, -675, \ldots
\][/tex]
