To determine which student's sequence is geometric, we need to examine the ratio between consecutive terms in each sequence. A sequence is geometric if the ratio between consecutive terms is constant.
### Angela's Sequence: [tex]\(-6, -9, -12, -15, \ldots\)[/tex]
Let's find the ratio between the consecutive terms:
[tex]\[
\frac{-9}{-6} = \frac{-3}{-2}
\][/tex]
[tex]\[
\frac{-12}{-9} = \frac{-4}{-3}
\][/tex]
[tex]\[
\frac{-15}{-12} = \frac{-5}{-4}
\][/tex]
The ratios are not equal ([tex]\(\frac{3}{2} \neq \frac{4}{3} \neq \frac{5}{4}\)[/tex]), so Angela's sequence is not geometric.
### Bradley's Sequence: [tex]\(-2, -6, -12, -24, \ldots\)[/tex]
Let's find the ratio between the consecutive terms:
[tex]\[
\frac{-6}{-2} = 3.0
\][/tex]
[tex]\[
\frac{-12}{-6} = 2.0
\][/tex]
[tex]\[
\frac{-24}{-12} = 2.0
\][/tex]
The ratios are not equal ([tex]\(3.0 \neq 2.0\)[/tex]), so Bradley's sequence is not geometric.
### Carter's Sequence: [tex]\(-1, -3, -9, -27, \ldots\)[/tex]
Let's find the ratio between the consecutive terms:
[tex]\[
\frac{-3}{-1} = 3.0
\][/tex]
[tex]\[
\frac{-9}{-3} = 3.0
\][/tex]
[tex]\[
\frac{-27}{-9} = 3.0
\][/tex]
The ratios are equal ([tex]\(3.0 = 3.0 = 3.0\)[/tex]), so Carter's sequence is geometric.
### Dominique's Sequence: [tex]\(-1, -3, -9, -81, \ldots\)[/tex]
Let's find the ratio between the consecutive terms:
[tex]\[
\frac{-3}{-1} = 3.0
\][/tex]
[tex]\[
\frac{-9}{-3} = 3.0
\][/tex]
[tex]\[
\frac{-81}{-9} = 9.0
\][/tex]
The ratios are not equal ([tex]\(3.0 \neq 9.0\)[/tex]), so Dominique's sequence is not geometric.
### Conclusion
Based on the analysis above, only Carter's sequence is geometric with a constant ratio of [tex]\(3.0\)[/tex].
