已知数列\(\{a _{n} \}\)满足\(|a _{n+1} -a _{n} |=2n+1\)．
\((1)\)若数列\(\{a _{n} \}\)的首项为\(a _{1}\)，其中\(0 < a _{1} < 3\)，且\(a _{1}\)，\(a _{2}\)，\(a _{3}\)构成公比小于\(0\)的等比数列，求\(a _{1}\)的值；
\((2)\)若\(a _{n}\)是公差为\(d(d > 0)\)的等差数列\(\{b _{n} \}\)的前\(n\)项和，求\(a _{1}\)的值；
\((3)\)若\(a _{1} =1\)，\(a _{2} =-2\)，且数列\(\{a _{2n-1} \}\)单调递增，数列\(\{a _{2n} \}\)单调递减，求数列\(\{a _{n} \}\)的通项公式．