组卷网>知识点选题>Sn和an关系法求数列通项
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1 . 数列eqId93e38ecd74a24cb59da79181b95bfd3a的前eqId5f904d1376ac4de7a7d6cfea92ff6981项和为eqIddb5a8358b9394663be91c8f58b409ccd,则eqId93e38ecd74a24cb59da79181b95bfd3a的通项公式是__________________.
2 . 已知正项数列eqId93e38ecd74a24cb59da79181b95bfd3a的前n项和为eqIddb5481de79c946c0a760143297d5eadeeqIdef51378d6b3048fc94aece7f1b93e1af,当eqId455a9040c3d646b8bc637ce6d7d7b9a4时,eqId96af0588ca3e49249ba07eb227946306eqIddb5481de79c946c0a760143297d5eadeeqIdd815a0f122e847c889673a050ceda7a0的等差中项.
(1)求数列eqId93e38ecd74a24cb59da79181b95bfd3a的通项公式;
(2)记eqId2fcee49a9d214101bece0fa628f8980a,求数列eqIdeeb4ca98872f4e6d91cea28f43fc0b63的前n项和eqId92ed363a54bd4a8a93df9463bb3af1f5.
3 . 设数列eqId93e38ecd74a24cb59da79181b95bfd3a的前n项和为eqIddb5481de79c946c0a760143297d5eade,且eqIda180e9c86c9d4e38beb2d6a45ad2912e,则eqId455f8053a7c54e04b611948d2918a681(   ).
A.12B.13C.16D.32
4 . 已知等比数列eqId93e38ecd74a24cb59da79181b95bfd3a的前eqId5f904d1376ac4de7a7d6cfea92ff6981项和为eqIddb5481de79c946c0a760143297d5eade,且当eqId6c2146ec6df54fc9af9b2aef04489c8b时,eqIddb5481de79c946c0a760143297d5eadeeqId553ca58289c44e7ba04606445f2b5015eqIdcf4f7a91e7f54b3382c06e2bfa6fb85a的等差中项(eqIda4be99d332154d13a4a6ed1ff6444fe7为实数).
(1)求eqIda4be99d332154d13a4a6ed1ff6444fe7的值及数列eqId93e38ecd74a24cb59da79181b95bfd3a的通项公式,
(2)令eqId5cc09118dc234b4ea8c440dafe6198a6,是否存在正整数eqId4d2187284c5d4de29906363f7d21f60f,使得eqIda3f30d87292a4a5285f9cbc53184c014对任意正整数eqId5f904d1376ac4de7a7d6cfea92ff6981均成立?若存在,求出eqId4d2187284c5d4de29906363f7d21f60f的最大值;若不存在,请说明理由.
5 . 已知数列eqId93e38ecd74a24cb59da79181b95bfd3a的前n项和eqIddb5481de79c946c0a760143297d5eade满足eqId213dac5ba2a041fc85141db50f2a8618,数列eqIdeeb4ca98872f4e6d91cea28f43fc0b63满足eqIdcb0f0b3b54874772aeee1f924171f0b4
(1)求数列eqId93e38ecd74a24cb59da79181b95bfd3aeqIdeeb4ca98872f4e6d91cea28f43fc0b63的通项公式;
(2)求数列eqId7463ac5c573d4f0fb0aa7dcc4e8eb2f4的前n项和eqId92ed363a54bd4a8a93df9463bb3af1f5
6 . 已知数列{an}的前n项和为Sn,满足Sn= 2an-1,nN*.数列{bn}满足nbn+1-(n+1)bn= nn+1),nN*,且b1= 1.
(1)求数列{an}和{bn}的通项公式;
(2)若eqId32ab4712ae4940b1b80bff84be0da4b3,数列{cn}的前n项和为Tn,对任意的nN*,都有Tn<nSn-a,求实数a的取值范围;
(3)是否存在正整数mn使b1ambnn> 1)成等差数列,若存在,求出所有满足条件的mn,若不存在,请说明理由.
7 . 已知数列eqId93e38ecd74a24cb59da79181b95bfd3a满足eqId8c7c4b8d2cd5414d80d1cedee8ba88a6,数列eqId93e38ecd74a24cb59da79181b95bfd3a的前eqId5f904d1376ac4de7a7d6cfea92ff6981项和为eqIddb5481de79c946c0a760143297d5eade,若______,在以下三个条件中任选一个条件填入横线上,完成问题(1)和(2):
eqIddb03396c799b4d429dfd5665e37ecd34
②数列eqId74ef5fe5183946caaee41d8974816a20满足:eqId23101adc4a11465e96d03dc1486281aeeqId1b870f8b46dc466aa4eb8cceaae660c7,且eqId74ef5fe5183946caaee41d8974816a20的前eqId5f904d1376ac4de7a7d6cfea92ff6981项和为eqId39539396b67c4a3197920c8c7a37dc34
eqId634901a014614b238eb21a2dab8a33f5
问题:
(1)求数列eqId93e38ecd74a24cb59da79181b95bfd3a的通项公式;
(2)数列eqIdeeb4ca98872f4e6d91cea28f43fc0b63是首项和公比均为2的等比数列,求数列eqId66a490934e3445f1b31fa060486cb4d0中有多少个小于2021的项.
填空题 | 较易(0.85) | 2021·上海市实验学校高一期末
8 . 数列eqId93e38ecd74a24cb59da79181b95bfd3a的前eqId5f904d1376ac4de7a7d6cfea92ff6981项和eqIdeeb75c0dd94a4b67b0e5c575028313fb,则其通项公式eqId38e7aab9632e418f8d07479b236353ec____________
9 . 已知数列eqId93e38ecd74a24cb59da79181b95bfd3a的前eqId5f904d1376ac4de7a7d6cfea92ff6981项和为eqIddb5481de79c946c0a760143297d5eadeeqId85cc2f6b0efd497d98c376b7c037d1fa,且eqId46c40578d65d4fe6b768b130aa3d6015
(1)求数列eqId93e38ecd74a24cb59da79181b95bfd3a的通项;
(2)设数列eqIdeeb4ca98872f4e6d91cea28f43fc0b63满足eqIdccf03ac8d2b94f3a8483a983d6b5d9cd,记eqIdeeb4ca98872f4e6d91cea28f43fc0b63的前eqId5f904d1376ac4de7a7d6cfea92ff6981项和为eqId92ed363a54bd4a8a93df9463bb3af1f5
①求eqId92ed363a54bd4a8a93df9463bb3af1f5
②若eqId9b02c5916a7942b8aa84262a7f15a826对任意eqId532dc4d959024b79b546428f5856e5aa恒成立,求实数eqId5f420ef2d0b94c4b8a5d8e20a5d1ce2c的取值范围.
10 . 设eqIddb5481de79c946c0a760143297d5eade是数列eqId93e38ecd74a24cb59da79181b95bfd3a的前eqId5f904d1376ac4de7a7d6cfea92ff6981项和,eqId77b3f6b9955e499dbdab033a38779496eqId61b8f8cf7484430b85dcea23a63e1d48,则下列说法正确的有(   )
A.数列eqId93e38ecd74a24cb59da79181b95bfd3a的前eqId5f904d1376ac4de7a7d6cfea92ff6981项和为eqIdb4d0489b1cdd4d9eae8fdd27e6fd782a
B.数列eqIda4a8f097158842c99246acee68ad20d3为递增数列
C.数列eqId93e38ecd74a24cb59da79181b95bfd3a的通项公式为eqIde58ff15611b848feb92245f5e48646db
D.数列eqId93e38ecd74a24cb59da79181b95bfd3a的最大项为eqId75691f28a5bb4c8287401017aa3a2d29
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