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1 . 己知等差数列eqId93e38ecd74a24cb59da79181b95bfd3a公差不为0,正项等比数列eqIdeeb4ca98872f4e6d91cea28f43fc0b63eqId28d7f97167974574a89dba2521c1ac74eqId6ce880dc0ee447159ae41a1414baac93,则以下命题中正确的是(   )
A.eqIdc33f65574b174ae08ba6ad2a647ed5daB.eqId9a03aea33e684e87a843129573abb724C.eqId3244c713ec204fcfbf80a907d2e95857D.eqId6a42b5888cc84a8280c1b7e8827946b5
单选题 | 一般(0.65) | 2020·上海松江区·高三一模
2 . 记eqIddb5481de79c946c0a760143297d5eade为数列eqId2c1230a9ef5a4968be599681d676dd2b的前项和,已知点eqId14c9042e5b5848fbaacccde154f7d5d3在直线eqId906475752d1b42c3825a334410bda009上,若有且只有两个正整数n满足eqId13123b61283c477ba6a297af4a5d057a,则实数k的取值范围是(   )
A.eqIde2482399c9134ad39d94f4f591d19c59B.eqId4a9bc5adef8d406f9c3b85346fb1992d
C.eqIddf27339258334a8eba41f6830e494b37D.eqIdf3c734da43de4a7a8ce95906d3287010
单选题 | 较难(0.4) | 2021·上海高三三模
3 . 若数列eqId93e38ecd74a24cb59da79181b95bfd3a满足:对任意eqId532dc4d959024b79b546428f5856e5aa,只有有限个正整数eqIda4be99d332154d13a4a6ed1ff6444fe7,使得eqId3e8b101ed19a4fd0b3b17e3cbdddfd36成立,记这样的eqIda4be99d332154d13a4a6ed1ff6444fe7的个数为eqId9055748522b042128e8a19716465748c,则得到一悠闲的数列eqId19ea714d1e90493f8aa2b3019e99c055,例如,若数列eqId93e38ecd74a24cb59da79181b95bfd3a是1,2,3,…,eqId5f904d1376ac4de7a7d6cfea92ff6981,…,则得数列eqId9055748522b042128e8a19716465748c是0,1,2,…,eqIdd7c5ded96af7486fa63823a1c0851afb,…,已知对任意的eqId532dc4d959024b79b546428f5856e5aaeqId245c4552fa804098945b4a058d99449a,则eqIdfded4c38428242679e07ee1432e5e346(   )
A.eqIdf764d6c3b9a74906a9432143744335caB.2014C.eqId6d3d76204f1e4667b0a23db3e9494e73D.2015
4 . 已知等差数列eqId93e38ecd74a24cb59da79181b95bfd3a的前n项和为SnnN*),公差d≠0,S6=90,a7a3a9的等比中项,则下列选项正确的是(   )
A.a1=22B.d=-2
C.当n=10或n=11时,Sn取得最大值D.当Sn>0时,n的最大值为20
单选题 | 困难(0.15) | 2020·全国高三专题练习(文)
5 . 已知数列eqId93e38ecd74a24cb59da79181b95bfd3a满足:eqId8c7c4b8d2cd5414d80d1cedee8ba88a6,且eqId3eb776b7cbfd441b9e6de465832ffcfa,下列说法正确的是(   )
A.若eqId681ee32b0980433e94ff5b7e029a5760,则eqId25a4b91dd48044d1858a068ede29c251B.若eqIde7aae36840e145a89dc0a24becae07af,则eqId405fc200ce4a428ca3f913bc97a0bde0
C.eqIddff1a30c12d4498eacf7b622703d119cD.eqId30ce5a2ae7914724a45dca5bc8f19dad
单选题 | 较易(0.85) | 2020·福建莆田二中高二月考
解题方法
7 . 如图是某省从3月1日至3月31日的新冠肺炎每日新增确诊病例变化曲线图.
说明: figure
若该省从3月1日至3月31日的新冠肺炎每日新增确诊人数按日期顺序排列构成数列{an},设数列{an}的前n项和为Sn,则下列有关数列{Sn}说法中正确的是(  )
A.数列{Sn}为先增后减数列B.数列{Sn}为递增数列
C.数列{Sn}的最大项是S12D.数列{Sn}的最大项是S31
单选题 | 较难(0.4) | 2020·浙江大学附属中学高三其他模拟
解题方法
8 . 已知正项数列eqId93e38ecd74a24cb59da79181b95bfd3a满足eqIdbabe8f70c7d14d949d1b835bf86c2e9deqId5cfa10abef5f4b9d9b63738fbdd3bfff则下列正确的是(   )
A.当eqId84baf5260a714df9a42e9e3daf01ca4a时,eqIdf29dfa3751db4e5a9c8fb2560ea8e5d8递增,eqIdec3c38c1b7b044209ad697bfca74706d递增
B.当eqId84baf5260a714df9a42e9e3daf01ca4a时,eqIdf29dfa3751db4e5a9c8fb2560ea8e5d8递增,eqIdec3c38c1b7b044209ad697bfca74706d递减
C.当eqIdaf0c28fa6a1e435ba5462b37418b2f99时,eqIdf29dfa3751db4e5a9c8fb2560ea8e5d8递增,eqIdec3c38c1b7b044209ad697bfca74706d递减
D.当eqIdaf0c28fa6a1e435ba5462b37418b2f99时,eqIdf29dfa3751db4e5a9c8fb2560ea8e5d8递减,eqIdec3c38c1b7b044209ad697bfca74706d递减
单选题 | 一般(0.65) | 2020·苍南县树人中学高一期中
9 . 已知数列eqId93e38ecd74a24cb59da79181b95bfd3a中,eqId5cfa10abef5f4b9d9b63738fbdd3bfffeqIdd29d6b89576f4b4fbbf1081a6724961c,下列说法正确的是(   )
A.当eqIde478b10f4c204f18a3fd6625f1017781时,eqId126bf1a48bb54756b5c506b15d926099B.当eqIde478b10f4c204f18a3fd6625f1017781时,eqId6f35ba6acc47481c9865a05696ff9a81
C.当eqIdd2245f820f0d44c7a32879a7c593fc4d最小时,有eqId06cc9b4949ce4809a05ce82e20fa6282D.当eqIdbc24c6e646ef45d78124b2ff20ca875b最大时,有eqId06cc9b4949ce4809a05ce82e20fa6282
填空题 | 较难(0.4) | 2020·黑山县黑山中学高三月考(理)
解题方法
典型
10 . 已知eqId75691f28a5bb4c8287401017aa3a2d29eqId0509add794484602a2c710f41d9ddddc,…,eqIdef9cef8e6d054d8dac46b8cde14953adeqId91527d9f559f45afb12460e0c2e33b6feqId802dd8e915624120aa727fb9b14978b0,…,eqId45a6b09a4fd24aecb1eafc7cf40bb354eqId5f904d1376ac4de7a7d6cfea92ff6981是正整数),令eqIdcc0670bd743c44fe90c30f2f025659a1eqId544916fb682b4c7b8a5f7f00ac3e529d,…,eqIdf0304ae9e87a440da499174a9500e945.某人用下图分析得到恒等式:
说明: figure
eqId4f6d327e1a8146b3996e1f39f34c6404,这个恒等式称为分部求和公式,也称阿贝尔变换.(注:阿贝尔(1802年8月5日—1829年4月6日))(挪威数学家)则eqIdb51fed17b2ed48cf9e0e9bb31fe0d54e______eqId83a2b48f6074478e987a806e83545275).
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