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            • 1.
              函数\(y= \sqrt {9-(x-5)^{2}}\)的图象上存在不同的三点到原点的距离构成等比数列,则以下不可能成为等比数列的公比的数是\((\)  \()\)
              A.\( \dfrac {3}{4}\)
              B.\( \sqrt {2}\)
              C.\( \sqrt {3}\)
              D.\( \sqrt {5}\)
            • 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.
            • 3.

              已知数列\(\left\{ {{a}_{n}} \right\}\)满足:\({{a}_{1}}=3\),\({{a}_{n+1}}=\dfrac{1}{1-{{a}_{n}}}\),则\({{a}_{2020}}=(\)    \()\)

              A. \(3\)
              B.\(-\dfrac{1}{2}\)
              C.\(\dfrac{2}{3}\)
              D.\(\dfrac{3}{2}\)
            • 4.

              已知数列\(\left\{{a}_{n}\right\} \)的通项\({a}_{n}= \dfrac{n}{{n}^{2}+17}(n∈{N}^{*}) \),则数列\(\left\{{a}_{n}\right\} \)的最大项是\((\)  \()\)

              A.第\(4\)项
              B.第\(5\)项
              C.第\(6\)项
              D.第\(4\)项或第\(5\)项
            • 5.

              已知数列\(\{a_{n}\}\)是递增数列,且对\(n∈N^{*}\),有\(a_{n}=n^{2}+λn \),则实数\(λ \)的取值范围是(    )

              A.\((- \dfrac{7}{2},+∞) \)
              B.\([0,+∞)\)
              C.\([-2,+∞)\)
              D.\((-3,+∞)\)
            • 6.
              已知数列\(\{a_{n}\}\)是首项为\(a_{1}= \dfrac {1}{4}\),公比\(q= \dfrac {1}{4}\)的等比数列,设\(b_{n}+2=3\log _{ \frac {1}{4}}a_{n}(n∈N^{*})\),数列\(\{c_{n}\}\)满足\(c_{n}=a_{n}⋅b_{n}\).
              \((1)\)求证:\(\{b_{n}\}\)是等差数列;
              \((2)\)求数列\(\{c_{n}\}\)的前\(n\)项和\(S_{n}\);
              \((3)\)若\(c_{n}\leqslant \dfrac {1}{4}m^{2}+m-1\)对一切正整数\(n\)恒成立,求实数\(m\)的取值范围.
            • 7.
              已知数列 满足 ,则 的最小值为\((\)    \()\)
              A.       
              B.          
              C.             
              D.
            • 8.
              已知数列\(\{a_{n}\}\)、\(\{b_{n}\}\)满足:\(a_{1}= \dfrac {1}{4}\),\(a_{n}+b_{n}=1\),\(b_{n+1}= \dfrac {b_{n}}{1-a_{n^{2}}}\).
              \((1)\)求\(a_{2}\),\(a_{3}\);
              \((2)\)证数列\(\{ \dfrac {1}{a_{n}}\}\)为等差数列,并求数列\(\{a_{n}\}\)和\(\{b_{n}\}\)的通项公式;
              \((3)\)设\(S_{n}=a_{1}a_{2}+a_{2}a_{3}+a_{3}a_{4}+…+a_{n}a_{n+1}\),求实数\(λ\)为何值时\(4λS_{n} < b_{n}\)恒成立.
            • 9.
              数列\(\{a_{n}\}\)满足:\(a_{n}=13-3n\),\(b_{n}=a_{n}⋅a_{n+1}⋅a_{n+2}\),\(S_{n}\)是\(\{b_{n}\}\)的前\(n\)项和,则\(S_{n}\)的最大值\((\)  \()\)
              A.\(280\)
              B.\(308\)
              C.\(310\)
              D.\(320\)
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