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            • 1.
              已知数列\(\{a_{n}\}\)满足\(a_{7}=15\),且点\((a_{n},a_{n+1})(n∈N^{*})\)在函数\(y=x+2\)的图象上.
              \((1)\)求数列\(\{a_{n}\}\)的通项公式;
              \((2)\)设\(b_{n}=3^{a_{n}}\),求数列\(\{b_{n}\}\)的前\(n\)项和\(T_{n}\).
            • 2.
              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.\( \sqrt {5}\)
            • 3.
              在数列\(1\),\(2\),\( \sqrt {7}, \sqrt {10}, \sqrt {13}\),\(…\)中,\(2 \sqrt {19}\)是这个数列的\((\)  \()\)
              A.第\(16\)项
              B.第\(24\)项
              C.第\(26\)项
              D.第\(28\)项
            • 4.
              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.
            • 5.

              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.\(\dfrac{3}{2}\)
            • 6.

              设\(f(n)=1+\dfrac{1}{2}+\dfrac{1}{3}+\cdots +\dfrac{1}{2n+1}(n\in {{N}^{*}})\),则\(n=1\)时,\(f(n)=\)(    )

              A.  \(1\)      
              B. \(\dfrac{1}{3}\)
              C.\(1+\dfrac{1}{2}+\dfrac{1}{3}\)
              D.以上答案都不对
            • 7. 已知数列\(\{a_{n}\}\)的前\(n\)项和为\(S_{n}\),点\((n,S_{n})(n∈N^{*})\)在函数\(y=2x^{2}+x\)的图象上,则数列\(\{a_{n}\}\)的通项公式为______.
            • 8.

              已知等差数列\(\{a_{n}\}\)中,已知\(a_{5} > 0\),\(a_{4}+a_{7} < 0\),那么使其前\(n\)项和\(S_{n}\)最大的\(n\)是(    )                                                    

              A.\(7\)                   
              B.\(6\)                    
              C.\(5\)             
              D.\(4\)
            • 9.

              已知数列\(\left\{ {{a}_{n}} \right\}\)的通项公式为\({a}_{n}={n}^{2}-2λn+1\left(n∈{N}^{*}\right) \),且数列\(\left\{ {{a}_{n}} \right\}\)为递增数列”,则\(\lambda \)的取值范围是_______________.

            • 10. 数列\(-1\),\( \dfrac {1}{2},- \dfrac {1}{3}, \dfrac {1}{4},- \dfrac {1}{5}…\)的一个通项公式为\((\)  \()\)
              A.\( \dfrac {(-1)^{n}}{n}\)
              B.\(- \dfrac {1}{n}\)
              C.\( \dfrac {(-1)^{n-1}}{n}\)
              D.\( \dfrac {1}{n}\)
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