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            • 1.
              设等差数列\(\{a_{n}\}\)满足:\(3a_{7}=5a_{13}\),\(\cos ^{2}a_{4}-\cos ^{2}a_{4}\sin ^{2}a_{7}+\sin ^{2}a_{4}\cos ^{2}a_{7}-\sin ^{2}a_{4}=-\cos (a_{5}+a_{6})\)公差\(d∈(2,0)\),则数列\(\{a_{n}\}\)的前项和\(S_{n}\)的最大值为\((\)  \()\)
              A.\(100π\)
              B.\(54π\)
              C.\(77π\)
              D.\(300π\)
            • 2.
              \(《\)九章算术\(》\)的盈不足章第\(19\)个问题中提到:“今有良马与驽马发长安,至齐\(.\)齐去长安三千里\(.\)良马初日行一百九十三里,日增一十三里\(.\)驽马初日行九十七里,日减半里\(…\)”其大意为:“现在有良马和驽马同时从长安出发到齐去\(.\)已知长安和齐的距离是\(3000\)里\(.\)良马第一天行\(193\)里,之后每天比前一天多行\(13\)里\(.\)驽马第一天行\(97\)里,之后每天比前一天少行\(0.5\)里\(…\)”试问前\(4\)天,良马和驽马共走过的路程之和的里数为\((\)  \()\)
              A.\(1235\)
              B.\(1800\)
              C.\(2600\)
              D.\(3000\)
            • 3.
              已知\(S_{n}\)是等差数列\(\{a_{n}\}\)的前\(n\)项和,且\(a_{3}=-6\),\(S_{5}=S_{6}\).
              \((\)Ⅰ\()\)求\(\{a_{n}\}\)的通项公式;
              \((\)Ⅱ\()\)若等比数列\(\{b_{n}\}\)满足\(b_{1}=a_{2}\),\(b_{2}=S_{3}\),求\(\{b_{n}\}\)的前\(n\)项和.
            • 4.
              已知\(\{a_{n}\}\)为等差数列,前\(n\)项和为\(S_{n}\),若\(a_{2}+a_{5}+a_{8}= \dfrac {π}{4}\),则\(\sin S_{9}=(\)  \()\)
              A.\( \dfrac {1}{2}\)
              B.\( \dfrac { \sqrt {2}}{2}\)
              C.\(- \dfrac {1}{2}\)
              D.\(- \dfrac { \sqrt {2}}{2}\)
            • 5.
              在等差数列\(\{a_{n}\}\)中,若\(S_{n}\)为前\(n\)项和,\(2a_{7}=a_{8}+5\),则\(S_{11}\)的值是\((\)  \()\)
              A.\(55\)
              B.\(11\)
              C.\(50\)
              D.\(60\)
            • 6.
              已知正项数列\(\{a_{n}\}\)满足:\(4S_{n}= a_{ n }^{ 2 }+2a_{n}-3\),其中\(S_{n}\)为数列\(\{a_{n}\}\)的前\(n\)项和.
              \((1)\)求数列\(\{a_{n}\}\)的通项公式;
              \((2)\)设\(b_{n}= \dfrac {1}{ a_{ n }^{ 2 }-1}\),求数列\(\{b_{n}\}\)的前\(n\)项和\(T_{n}\).
            • 7.
              已知数列\(\{a_{n}\}\)的前\(n\)项和为\(S_{n}\),\(a_{1}= \dfrac {1}{2}\),\(2a_{n+1}=S_{n}+1\).
              \((\)Ⅰ\()\)求\(a_{2}\),\(a_{3}\)的值;
              \((\)Ⅱ\()\)设\(b_{n}=2a_{n}-2n-1\),求数列\(\{b_{n}\}\)的前\(n\)项和\(T_{n}\).
            • 8.
              已知等差数列\(\{a_{n}\}\)的前\(n\)项和为\(S_{n}\),\(a_{3}=7\),\(S_{9}=27\).
              \((1)\)求数列\(\{a_{n}\}\)的通项公式;
              \((2)\)若\(b_{n}=|a_{n}|\),求数列\(\{b_{n}\}\)的前\(n\)项和\(T_{n}\).
            • 9.
              若数列\(A\):\(a_{1}\),\(a_{2}\),\(…\),\(a_{n}(n\geqslant 3)\)中\(a_{i}∈N^{*}(1\leqslant i\leqslant n)\)且对任意的\(2\leqslant k\leqslant n-1\),\(a_{k+1}+a_{k-1} > 2a_{k}\)恒成立,则称数列\(A\)为“\(U-\)数列”.
              \((1)\)若数列\(1\),\(x\),\(y\),\(7\)为“\(U-\)数列”,写出所有可能的\(x\)、\(y\);
              \((2)\)若“\(U-\)数列”\(A\):\(a_{1}\),\(a_{2}\),\(…\),\(a_{n}\)中,\(a_{1}=1\),\(a_{n}=2017\),求\(n\)的最大值;
              \((3)\)设\(n_{0}\)为给定的偶数,对所有可能的“\(U-\)数列”\(A\):\(a_{1}\),\(a_{2}\),\(…\),\(a_{n_{0}}\),记\(M=max\{a_{1},a_{2},…,a_{n_{0}}\}\),其中\(max\{x_{1},x_{2},…,x_{s}\}\)表示\(x_{1}\),\(x_{2}\),\(…\),\(x_{s}\)这\(s\)个数中最大的数,求\(M\)的最小值.
            • 10.
              已知数列\(\{a_{n}\}\)满足\(5^{a_{n+1}}=25\cdot 5^{a_{n}}\),且\(a_{2}+a_{4}+a_{6}=9\),则\(\log _{ \frac {1}{3}}(a_{5}+a_{7}+a_{9})=(\)  \()\)
              A.\(-3\)
              B.\(3\)
              C.\(- \dfrac {1}{3}\)
              D.\( \dfrac {1}{3}\)
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