[tex]\displaystyle a_1=2,~a_{30}=60,~S_{20}=? \\ \\ a_{30}=60 \Rightarrow a_{30-1}+r=60 \Rightarrow a_{29}+r=60 \Rightarrow a_1+29r=60 \Rightarrow \\ \\ \Rightarrow 2+29r=60 \Rightarrow 29r=60-2 \Rightarrow29r=58 \Rightarrow r= \frac{58}{29} \Rightarrow r=2 \\ \\ S_{20}= \frac{2 \cdot 2+(20-1) \cdot 2}{2} \cdot 20 \Rightarrow S_{20}= (4+19 \cdot 2) \cdot 10 \Rightarrow \\ \\ \Rightarrow S_{20}=(4+ 38) \cdot 10 \Rightarrow S_{20}=42 \cdot 10 \Rightarrow \boxed{S_{20}=420}[/tex]
