To determine which student's sequence represents a geometric sequence, we need to identify the sequences where the ratio between consecutive terms is constant. Let's look at each student's sequence in turn.
1. Andre's Sequence:
[tex]\[
-\frac{3}{4}, \frac{3}{8}, -\frac{3}{16}, -\frac{3}{32}, \ldots
\][/tex]
To be a geometric sequence, the ratio between each pair of consecutive terms must be constant.
2. Brenda's Sequence:
[tex]\[
\frac{3}{4}, -\frac{3}{8}, \frac{3}{16}, \frac{3}{32}, \ldots
\][/tex]
Again, we need to determine if the ratios are constant.
3. Camille's Sequence:
[tex]\[
\frac{3}{4}, \frac{3}{8}, -\frac{3}{16}, -\frac{3}{32}, \ldots
\][/tex]
Checking for a constant ratio between terms.
4. Doug's Sequence:
[tex]\[
\frac{3}{4}, -\frac{3}{8}, \frac{3}{16}, -\frac{3}{32}, \ldots
\][/tex]
Verifying if each term is obtained by multiplying the previous term by a constant ratio.
After reviewing the sequences, it turns out that Doug's sequence is the one with a constant ratio between each pair of consecutive terms, which means Doug wrote a geometric sequence.
Conclusion:
Doug is the student who wrote a geometric sequence.
