已知数列\(\{a _{n} \}\)满足\(a _{n+2} +a _{n} =2a _{n+1} (n∈N ^{*} )\)，数列\(\{b _{n} \}\)满足\(\dfrac{{{b}_{n+1}}}{{{b}_{n}}}={{a}_{n+1}}-{{a}_{n}} (n∈N ^{*} )\)，且\(a _{1} =b _{1}\)，\(a _{3} =5\)，\(a _{5} +a _{7} =22\)．

\((1)\)求\(a _{n}\)及\(b _{n}\)；

\((2)\)令\(c _{n} =a _{n} b _{n}\)，\(n∈N ^{*}\)，求数列\(\{c _{n} \}\)的前\(n\)项和\(S _{n}\)．