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Sagot :
The given geometric sequence:
[tex]-0.125,0.25,-0.5,1,-2,...[/tex]The formula for the nth term of a geometric sequence whose first term is 'a' and common ratio is 'r' is:
[tex]a_n=ar^{n-1}[/tex]where,
[tex]\begin{gathered} n=number\text{ of terms} \\ a=first\text{ term} \end{gathered}[/tex]Given:
[tex]\begin{gathered} a=-0.125 \\ a_2=ar^{2-1}=ar=0.25 \\ a_3=ar^{3-1}=ar^2=-0.5 \end{gathered}[/tex]Hence, the common ratio is
[tex]\begin{gathered} \frac{second\text{ term}}{first\text{ term}}=\frac{third\text{ term}}{second\text{ term}} \\ \frac{0.25}{-0.125}=\frac{-0.5}{0.25} \\ -2=-2 \end{gathered}[/tex]Therefore, the common ratio(r) is
[tex]-2[/tex]
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