A geometric sequence is obtained by multiplying each term of the sequence by a constant. This constant is called the "common ratio".
[tex]x_n=ar^{(n-1)}[/tex]Given a geometric sequence, you can determine the common ratio by dividing one term of the sequence by the previous term.
[tex]r=\frac{a_n}{a_{n-1}}[/tex]The given sequence is
[tex]\mleft\lbrace-15,135,-1215\mright\rbrace[/tex]Select two consecutive terms, for example, the third and second terms, and divide them to determine the common ratio:
[tex]\begin{gathered} r=\frac{a_3}{a_2} \\ r=\frac{-1215}{135} \\ r=-9 \end{gathered}[/tex]The common ratio of the geometric sequence is r= -9
