[tex]\displaystyle a_3=5,~a_6=11,~a_{14}=? \\ a_3=5 \Rightarrow a_{3-1}+r=5 \Rightarrow a_2+r=5 \Rightarrow a_1+2r=5 \Rightarrow a_1=5-2r \\ a_6=11 \Rightarrow a_{6-1}+r=11 \Rightarrow a_5+r=11 \Rightarrow a_1+5r=11 \Rightarrow \\ \Rightarrow 5-2r+5r=11 \Rightarrow -2r+5r=11-5 \Rightarrow 3r=6 \Rightarrow r=2 \\ a_1=5-2r \Rightarrow a_1=5-2 \cdot 2 \Rightarrow a_1=5-5 \Rightarrow a_1=1 \\ a_{14}=a_{14-1}+r \Rightarrow a_{14}=a_{13}+r \Rightarrow a_{14}=a_1+13r \Rightarrow [/tex]
[tex]\displaystyle \Rightarrow a_{14}=1+13 \cdot 2 \Rightarrow a_{14}=1+26 \Rightarrow \boxed{a_{14}=27}[/tex]
