2.
如果\(n\)项有穷数列\(\{a_{n}\}\)满足\(a_{1}=a_{n}\),\(a_{2}=a_{n-1}\),\(…\),\(a_{n}=a_{1}\),即\(a_{i}=a_{n-i+1}(i=1,2,…,n)\),则称有穷数列\(\{a_{n}\}\)为“对称数列”\(.\)例如,由组合数组成的数列\( C_{ n }^{ 0 }, C_{ n }^{ 1 },…, C_{ n }^{ n-1 }, C_{ n }^{ n }\)就是“对称数列”.
\((\)Ⅰ\()\)设数列\(\{b_{n}\}\)是项数为\(7\)的“对称数列”,其中\(b_{1}\),\(b_{2}\),\(b_{3}\),\(b_{4}\)成等比数列,且\(b_{2}=3\),\(b_{5}=1.\)依次写出数列\(\{b_{n}\}\)的每一项;
\((\)Ⅱ\()\)设数列\(\{c_{n}\}\)是项数为\(2k-1(k∈N^{*}\)且\(k\geqslant 2)\)的“对称数列”,且满足\(|c_{n+1}-c_{n}|=2\),记\(S_{n}\)为数列\(\{c_{n}\}\)的前\(n\)项和;
\((ⅰ)\)若\(c_{1}\),\(c_{2}\),\(…c_{k}\)是单调递增数列,且\(c_{k}=2017.\)当\(k\)为何值时,\(S_{2k-1}\)取得最大值?
\((ⅱ)\)若\(c_{1}=2018\),且\(S_{2k-1}=2018\),求\(k\)的最小值.