[tex]\displaystyle a_2=3,~a_5=6 \\ a).a_1=?,~r=? \\ a_2=3 \Rightarrow
a_{2-1}+r=3 \Rightarrow a_1+r=3 \Rightarrow a_1=3-r \\ a_5=6 \Rightarrow
a_{5-1}+r=6 \Rightarrow a_4+r=6 \Rightarrow a_1+4r=6 \Rightarrow \\
\Rightarrow 3-r+4r=6 \Rightarrow -r+4r=6-3 \Rightarrow 3r=3 \Rightarrow
r= \frac{3}{3} \Rightarrow \boxed{r=1} \\ a_1=3-r \Rightarrow a_1=3-1
\Rightarrow \boxed{a_1=2} [/tex]
[tex]\displaystyle b).S_{20}=? ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\boxed{S_n= \frac{2a_1+(n-1) \cdot r}{2}\cdot n } \\ ~S_{20}= \frac{2 \cdot 2+(20-1) \cdot 1}{\not2} \cdot \not20 \Rightarrow S_{20}=(4+19 \cdot 1) \cdot 10 \Rightarrow \\ \Rightarrow S_{20}=(4+19) \cdot 10 \Rightarrow S_{20}=23 \cdot 10 \Rightarrow \boxed{S_{20}=230} [/tex]
