\((1)\)若\(x{,}y\)满足约束条件\(\begin{cases} x{+}y{-}5{\leqslant }0 \\ 2x{-}y{-}1{\geqslant }0 \\ x{-}2y{+}1{\leqslant }0 \end{cases}\)，则\(z{=}2x{+}y\)的最小值为______ ．

\((2)\) 设等比数列\(\{ a_{n}\}\)满足\(a_{1}{+}a_{3}{=}10{,}a_{2}{+}a_{4}{=}5\)，则\(a_{1}a_{2}{…}a_{n}\)的最大值为______ ．

\((3)\)设\(a{ > }0{,}b{ > }1\)，若\(a{+}b{=}2\)，则\(\dfrac{4}{a}{+}\dfrac{1}{b{-}1}\)的最小值为______ ．

\((4)\)在数列\(\{ a_{n}\}\)中，\(a{{ }}_{2}{=}\dfrac{3}{2}{,}a_{3}{=}\dfrac{7}{3}\)，且数列\(\{ na_{n}{+}1\}\)是等差数列，则\(a_{n}{=}\) ______ ．