定义：从一个数列\(\{a_{n}\}\)中抽取若干项\((\)不少于三项\()\)按其在\(\{a_{n}\}\)中的次序排列的一列数叫做\(\{a_{n}\}\)的子数列，成等差\((\)等比\()\)的子数列叫做\(\{a_{n}\}\)的等差\((\)等比\()\)子列．
\((1)\)记数列\(\{a_{n}\}\)的前\(n\)项和为\(S_{n}\)，已知\(S_{n}=n^{2}\)，求证：数列\(\{a_{3n}\}\)是数列\(\{a_{n}\}\)的等差子列；
\((2)\)设等差数列\(\{a_{n}\}\)的各项均为整数，公差\(d\neq 0\)，\(a_{5}=6\)，若数列\(a_{3}\)，\(a_{5}\)，\(a\;_{n_{1}}\)是数列\(\{a_{n}\}\)的等比子列，求\(n_{1}\)的值；
\((3)\)设数列\(\{a_{n}\}\)是各项均为实数的等比数列，且公比\(q\neq 1\)，若数列\(\{a_{n}\}\)存在无穷多项的等差子列，求公比\(q\)的所有值．