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填空题 | 一般(0.65) | 2021·河南高三月考(理)
1 . 将数列eqId5a7ee30b7765459aacf48f3b27f2d195eqId9f33dd6388de49e9920604c34776f6b2的公共项从小到大排列得到数列eqId8820b84c18ba449285611300628d34b1,则其通项eqId38e7aab9632e418f8d07479b236353ec___________.
2 . 已知eqIdcfc11fbc354c4e78ad195086f781ba8b,则eqId194a949c5b4b4cbeb212fb6b67c4a404的值为(   )
A.eqIdc275aff9bf6e43a68ec76defc8b582baB.eqIdc14e31598ba946ecb74ef3970711d186C.eqIde91960a5c7cf4f1cb9a4143199f04986D.不存在
3 . (1)已知等差数列eqId93e38ecd74a24cb59da79181b95bfd3a满足eqIda5665ef7f92b430ba697d0dbe2bb97a4,且eqIdac3623ae9adf49b4a197e6fda358d0c8,若数列eqIdc4420a2e686041ffa0e025db13358ebe的前eqId92478644b29a4a0e8470a8c89d31b49f项和为eqIddb5481de79c946c0a760143297d5eade,求eqId9c18823081b74ac0ab5d5a5c1ab00080的值.
(2)已知数列eqIdeeb4ca98872f4e6d91cea28f43fc0b63的前eqId92478644b29a4a0e8470a8c89d31b49f项和eqId92ed363a54bd4a8a93df9463bb3af1f5满足eqIdffbd5e577d12474181aaed4254439b2a,若eqIda5e80310b17d46f086f19bdbacfa6284,求eqId4b1710a68b3f42f3906f13e59388b864的值.
解答题 | 较难(0.4) | 2020·上海上外附中高二月考
4 . 对于无穷数列eqId46dd7fd51146439da45fc5731c33333c,若正整数eqId0af3cc7bf89043019788e3e371917a68,使得eqIdcd90fdfec7a1441db080a166bbfa4532时,有eqId6a9a158dbda741468114791ef315f18a,则称eqId46dd7fd51146439da45fc5731c33333c为“eqId0af3cc7bf89043019788e3e371917a68~不减数列”.
(1)设eqIdacdbb6893b0e4deea7200c6118cfdee9为正整数,且eqId3d94f1c02ae046ecacc0e504fd4cda4c,甲:eqId13eb2908e50945b5802917d3108bb405为“eqId08191f2c12324f94b4ddfe2f324a71cf~不减数列”.乙:eqId13eb2908e50945b5802917d3108bb405为“eqId69f56ef2c88b4b73a560da59f5247a82~不减数列”.设判断命题:“甲是乙的充分条件”的真假,并说明理由;
(2)已知函数eqId144eff5c0e4649138a21f2b1b6a06907与函数eqId66c854fc655f4a88a876c7162bd38bf3的图像关于直线eqIdf4cf79cbbea14d298940773ea43ed467对称,数列eqId93e38ecd74a24cb59da79181b95bfd3a满足eqId5905c2cfb2e9414d895079f9c197efe8,如果eqId93e38ecd74a24cb59da79181b95bfd3a为“eqId0af3cc7bf89043019788e3e371917a68~不减数列”,试求eqId0af3cc7bf89043019788e3e371917a68的最小值.
解答题 | 较难(0.4) |
5 . 已知无穷数列eqId2c1230a9ef5a4968be599681d676dd2b的首项为eqId75691f28a5bb4c8287401017aa3a2d29,其前eqId92478644b29a4a0e8470a8c89d31b49f项和为eqIddb5481de79c946c0a760143297d5eade,且eqId8f75883bb9b441fc9dc00784fb3b1098eqId3afc948462594e948ab9e7c0ba3580e4),其中eqId096e32e1d18145d199ccbacb5a9a85fe为常数且eqIda4e0e0457a474389a594bb7252ae40a8
(1)设eqIdc90749508ff24b43a1aacc0ef6f2f165,求数列eqId2c1230a9ef5a4968be599681d676dd2b的通项公式,并求eqId74e74ca9e79b4d8d93a7e9544f7afbff的值;
(2)设eqIdbced0b9ac0b043ceb5dea8bec65b3b89eqId5d320d06155e4113ae0bb01961fddc2d,是否存在正整数eqId4d2187284c5d4de29906363f7d21f60f使得数列eqId99f5d55075e347b9ae990fa3cdc9ecc0中的项eqIdfcae900647fb4e6ebdbc3aeb78fe76d8成立?若存在,求出满足条件eqId4d2187284c5d4de29906363f7d21f60f的所有值;若不存在,请说明理由.
(3)求证:数列eqId2c1230a9ef5a4968be599681d676dd2b中不同的两项之和仍为此数列中的某一项的充要条件为存在整数eqIda4be99d332154d13a4a6ed1ff6444fe7eqId38519f366e2547cab9d5080157adf620,使得eqIdc7190d983b10437c9159050d01c1efe4
更新:2021/01/05组卷:167
单选题 | 较难(0.4) | 2020·浙江高三月考
7 . 已知正项数列eqId93e38ecd74a24cb59da79181b95bfd3a,满足eqId37ad132f49f34f08bfba8caad75b39cdeqIdc73ad4de0ec14cba91db08ec61124907eqId5cfa10abef5f4b9d9b63738fbdd3bfff,则下列说法正确的是(   )
A.存在有理数a,对任意正整数m,都有eqIde8c1ec5574024257baff6e32859a6545
B.对于任意有理数a,存在正整数m,使得eqIdd76ad589e2f640188a75ff1c160be0fc
C.存在无理数a与正整数m,使得eqIdd76ad589e2f640188a75ff1c160be0fc
D.对于任意无理数a,存在正整数m,使得eqIdd76ad589e2f640188a75ff1c160be0fc
8 . 已知eqId054d5a7de5684002909fe944c86227c2是公比为整数的等比数列,设eqIdf3b2bbb0c49b44e5b4e1acebe99d682beqId9286163a63004a53a7334dc742be02d2,且eqId1e7157e19e92435cbafb9bc42cc03028,记数列eqId69fa66742e6b480eb0e55f574b8b7749的前eqId92478644b29a4a0e8470a8c89d31b49f项和为eqIddb5481de79c946c0a760143297d5eade,若eqIdc294d08f5a704ff0b2a408c0b09260c9,则eqId92478644b29a4a0e8470a8c89d31b49f的最小值为(   )
A.11B.10C.9D.8
解答题 | 较难(0.4) | 2020·全国高三专题练习
10 . 已知数列eqId93e38ecd74a24cb59da79181b95bfd3a满足:eqIdda0a11f8e32f431e8d43640d3755bf1c(常数eqId4f5682ff18d8421ab17ef168f54ca081),eqIdabbe063def3f46d1bd10dc573b6b9f13eqId9277a91d918447219d400b2439c236caeqId3e824472cf9f4d9bb0657a2101d2a534).数列eqIdeeb4ca98872f4e6d91cea28f43fc0b63满足:eqId04249057c1a44b1ca930aadf143e0579eqId3e824472cf9f4d9bb0657a2101d2a534).
(1)求eqId91527d9f559f45afb12460e0c2e33b6feqId802dd8e915624120aa727fb9b14978b0的值;
(2)求数列eqIdeeb4ca98872f4e6d91cea28f43fc0b63的通项公式;
(3)是否存在k,使得数列eqId93e38ecd74a24cb59da79181b95bfd3a的每一项均为整数?若存在,求出k的所有可能值;若不存在,请说明理由.
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