[tex]\displaystyle a_1=3,~a_{10}=12,~r=?,~S_{57}=? \\ \\ a_{10}=12 \Rightarrow a_{10-1}+r=12 \Rightarrow a_9+r=12 \Rightarrow a_1+9r=12 \Rightarrow \\ \\ \Rightarrow 3+9r=12 \Rightarrow 9r=12-3 \Rightarrow 9r=9 \Rightarrow r= \frac{9}{9} \Rightarrow \boxed{r=1} \\ \\ S_{57}= \frac{2 \cdot 3+(57-1) \cdot 1}{2} \cdot 57 \\ \\ S_{57}= \frac{6+56 \cdot 1}{2} \cdot 57 \\ \\ S_{57}= \frac{6+56}{2} \cdot 57 \\ \\ S_{57}= \frac{62}{2} \cdot 57 \\ \\ S_{57}=31 \cdot 57 \\ \\ \boxed{S_{57}=1767}[/tex]
