Resposta :
[tex]a_{11}=a_1+(11-1)\cdot R[/tex]
[tex]-100=200+(10)\cdot R\rightarrow-300=10\cdot R\rightarrow R=\frac{-300}{10}=-30[/tex]
[tex]a_{11} = a_1 + 10r \\ - 100 = 200 + 10r \\ - 10r = 200 + 100 \\ - 10r = 300 \\ r = \frac{300}{- 10} \\ \boxed{r = - 30}[/tex]