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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.
              已知数列\(\{a_{n}\}\)的前\(n\)项和为\(S_{n}\),且满足\(S_{n}=2a_{n}-n\).
              \((1)\)求证\(\{a_{n}+1\}\)为等比数列;
              \((2)\)求数列\(\{S_{n}\}\)的前\(n\)项和\(T_{n}\).
            • 3.
              设\(\{a_{n}\}\)是等差数列,\(\{b_{n}\}\)是各项都为正数的等比数列,且\(a_{1}=b_{1}=1\),\(a_{3}+b_{5}=21\),\(a_{5}+b_{3}=13\).
              \((\)Ⅰ\()\)求\(\{a_{n}\}\)、\(\{b_{n}\}\)的通项公式;
              \((\)Ⅱ\()\)求数列\(\{ \dfrac {a_{n}}{b_{n}}\}\)的前\(n\)项和\(S_{n}\).
            • 4.
              记\(S_{n}\)为等差数列\(\{a_{n}\}\)的前\(n\)项和,\(S_{5}=15a_{5}\),\(S_{5}-S_{2}=18\),则\(3a_{3}-a_{4}\)的值为\((\)  \()\)
              A.\(21\)
              B.\(24\)
              C.\(27\)
              D.\(30\)
            • 5.
              在等比数列\(\{a_{n}\}\)中,\(a_{1}=1\),\(a_{5}=4\),则\(a_{3}=(\)  \()\)
              A.\(2\)
              B.\(-2\)
              C.\(±2\)
              D.\( \sqrt {2}\)
            • 6.
              已知正项等比数列\(\{a_{n}\}\)满足:\(a_{7}=a_{6}+2a_{5}\),若存在两项\(a_{m}\),\(a_{n}\),使得\(a_{m}a_{n}=16a_{1}^{2}\),则\( \dfrac {1}{m}+ \dfrac {4}{n}\)的最小值为\((\)  \()\)
              A.\( \dfrac {3}{2}\)
              B.\( \dfrac {5}{3}\)
              C.\( \dfrac {25}{6}\)
              D.不存在
            • 7.
              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.
            • 8.

              数列\({ }\!\!\{\!\!{ }{{a}_{n}}{ }\!\!\}\!\!{ }\)是公比为\(2\)的等比数列,其前\(n\)项和为\({{S}_{n}}.\)若\({{a}_{2}}=\dfrac{1}{2}\),则\({{a}_{n}}=\)____;\({{S}_{5}}=\)____.

            • 9.

              已知在等比数列\(\{{{a}_{n}}\}\)中,\({{a}_{1}}=1\),且\({{a}_{2}}\)是\({{a}_{1}}\)和\({{a}_{3}}-1\)的等差中项.

              \((1)\)求数列\(\{{{a}_{n}}\}\)的通项公式;

              \((2)\)若数列\(\{{{b}_{n}}\}\)满足\({{b}_{n}}=2n-1+{{a}_{n}}(n\in {{N}^{*}})\),求\(\{{{b}_{n}}\}\)的前\(n\)项和\({{S}_{n}}\).

            • 10.
              设等比数列\(\{a_{n}\}\)满足公比\(q∈N^{*}\),\(a_{n}∈N^{*}\),且\(\{a_{n}\}\)中的任意两项之积也是该数列中的一项,若\(a_{1}=2^{81}\),则\(q\)的所有可能取值的集合为 ______ .
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