已知\(\{a_{n}\}\)是等差数列，\(a_{2}=4\)，\(S_{5}=35\)，且\(a_{1}\)，\(a_{k}(k\in N^{*})\)，\(a_{6}\)是等比数列\(\{b_{n}\}\)的前三项．
\((1)\)求数列\(\{a_{n}\}\)，\(\{b_{n}\}\)的通项公式；
\((2)\)数列\(c_{n}=\begin{cases}{a_{n},n\text{为奇数}}\\ {\sqrt[4]{b_{n}},n\text{为偶数}}\end{cases}\)，求数列\(\{c_{n}\}\)的前\(20\)项的和．