A geometric sequence is a sequence of
numbers where each term after the first is found by multiplying the
previous one by a fixed, non-zero number called the common ratio.
The common ration is obtained by dividing the a term by the preceding term.
Given that four
students wrote sequences during math class with
Andre writing [tex] -\frac{3}{4} ,\frac{3}{8} ,-\frac{3}{16} ,-\frac{3}{32} , . . .[/tex]
Brenda
writing [tex] \frac{3}{4} ,-\frac{3}{8} ,\frac{3}{16} ,\frac{3}{32} , . . .[/tex]
Camille writing [tex] \frac{3}{4} ,\frac{3}{8} ,-\frac{3}{16} ,-\frac{3}{32} , . . .[/tex]
Doug writing [tex] \frac{3}{4} ,-\frac{3}{8} ,\frac{3}{16} ,-\frac{3}{32} , . . .[/tex]
Notice that the common ratio for the four students is [tex]- \frac{1}{2} [/tex].
For Andre, the last term is wrong and hence his sequence is not a geometric sequence.
For Brenda, the last term is wrong and hence her sequence is not a geometric sequence.
For Camille, her sequence is not a geometric sequence.
For Doug, his sequence is a geometric sequence with a common ratio of [tex]- \frac{1}{2} [/tex].
Therefore, Doug wrote a geometric sequence.
