优优班--学霸训练营 > 知识点挑题
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            • 1.

              已知\(a_{n+1}-a_{n}-3=0\),则数列\(\{a_{n}\}\)是\((\)  \()\)

              A.递增数列                 
              B.递减数列

              C.常数列                                    
              D.摆动数列
            • 2. 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.\( \dfrac {1}{n}\)
            • 3.

              在小时候,我们就用手指练习过数数,一个小朋友按如图所示的规则练习数数,则大拇指对应的第\(253\)个数是________.

            • 4.

              已知数列\(\{{{a}_{n}}\}\)满足\({{a}_{1}}=1,{{a}_{2}}=1,{{a}_{n+1}}=|{{a}_{n}}-{{a}_{n-1}}|(n\geqslant 2)\), 则该数列前\(2017\)项的和等于\((\) \()\)

              A.\(1342\)        
              B.\(1343\)           
              C.\(1344\)           
              D.\(1345\)
            • 5.
              已知数列\(\{a_{n}\}\)的前\(n\)项和\(S_{n}=3n^{2}+8n(n∈N*)\),则\(\{a_{n}\}\)的通项公式为\((\)  \()\)
              A.\(a_{n}=6n+8\)
              B.\(a_{n}=6n+5\)
              C.\(a_{n}=3n+8\)
              D.\(a_{n}=3n+5\)
            • 6.

              设等比数列\(\left\{ {{a}_{n}} \right\}\)的公比为\(q\),前\(n\)项和为\({{T}_{n}}.(\)   \()\)


              A.若\(q > 1\),则数列\(\left\{ {{T}_{n}} \right\}\)单调递增     
              B.若数列\(\left\{ {{T}_{n}} \right\}\)单调递增,则\(q > 1\)                                                                                                                                                                                 
              C.若\({{T}_{n}} > 0\),则数列\(\left\{ {{T}_{n}} \right\}\)单调递增     
              D.若数列\(\left\{ {{T}_{n}} \right\}\)单调递增,则\({{T}_{n}} > 0\)
            • 7.

              已知等差数列\(\left\{ {{a}_{n}} \right\}\)中,\({{S}_{n}}\)是它的前\(n\)项和,若\({{S}_{16}} > 0\),且\({{S}_{17}} < 0\),则当\({{S}_{n}}\)取最大值时的\(n\)值为\((\)     \()\)

              A.\(7\)   
              B.\(8\)   
              C.\(9\)   
              D.\(16\)
            • 8.

              已知数列的通项公式为\({a}_{n}=(-1{)}^{n} \dfrac{n}{n+1} \)\({a}_{3}= \)\((\)    \()\)

              A.\(- \dfrac{2}{3} \)
              B.\( \dfrac{3}{4} \)
              C..\(- \dfrac{3}{4} \)
              D.\( \dfrac{2}{3} \)
            • 9.
              已知数列\(\{a_{n}\}\)中,\(a_{1}= \dfrac {3}{5},a_{n}=2- \dfrac {1}{a_{n-1}}(n\geqslant 2,n\in N*)\),数列\(\{b_{n}\}\)满足\(b_{n}= \dfrac {1}{a_{n}-1}(n\in N*)\).
              \((1)\)求证:数列\(\{b_{n}\}\)是等差数列;
              \((2)\)求数列\(\{a_{n}\}\)中的最大项和最小项,并说明理由.
            • 10.
              设数列\(\{a_{n}\}\)是公比小于\(1\)的正项等比数列,\(S_{n}\)为数列\(\{a_{n}\}\)的前\(n\)项和,已知\(S_{2}=12\),且\(a_{1}\),\(a_{2}+1\),\(a_{3}\)成等差数列.
              \((1)\)求数列\(\{a_{n}\}\)的通项公式;
              \((2)\)若\(b_{n}=a_{n}⋅(n-λ)\),且数列\(\{b_{n}\}\)是单调递减数列,求实数\(λ\)的取值范围.
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