组卷网>知识点选题>前n项和法判断等差数列
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多选题 | 一般(0.65) | 2022·全国高三专题练习
1 . 已知数列eqId93e38ecd74a24cb59da79181b95bfd3a的前eqId5f904d1376ac4de7a7d6cfea92ff6981项和为eqIddb5481de79c946c0a760143297d5eade,下列说法正确的是(   )
A.若eqId7ab8bbc05abf48d2a1ae12f212fba884,则eqId93e38ecd74a24cb59da79181b95bfd3a是等差数列
B.若eqIdcaf5d4fb02c34b2eaee0641499114e44,则eqId93e38ecd74a24cb59da79181b95bfd3a是等比数列
C.若eqId93e38ecd74a24cb59da79181b95bfd3a是等差数列,则eqId1643644c71d94e83b60f42a9528e9d22
D.若eqId93e38ecd74a24cb59da79181b95bfd3a是等比数列,且eqId6a66565cb50049aa9ca1ffd617abe7a3eqIdcf86a3efea6a4f738de6634cd0fe6ad3,则eqId5120239ca7bc48a5901fbadfdb6e5134
解答题 | 较易(0.85) | 2021·全国
同步
2 . 已知数列eqId93e38ecd74a24cb59da79181b95bfd3a的前eqId5f904d1376ac4de7a7d6cfea92ff6981项和eqId28df823e0a53426f80f1b5d837ca3a07,判断eqId93e38ecd74a24cb59da79181b95bfd3a是否为等差数列.
多选题 | 较易(0.85) | 2021·全国高三专题练习
3 . 已知数列eqId93e38ecd74a24cb59da79181b95bfd3a的前eqId5f904d1376ac4de7a7d6cfea92ff6981项和为eqIddb5481de79c946c0a760143297d5eade,下列说法正确的是(   )
A.若eqId7ab8bbc05abf48d2a1ae12f212fba884,则eqId93e38ecd74a24cb59da79181b95bfd3a是等差数列
B.若eqIdcaf5d4fb02c34b2eaee0641499114e44,则eqId93e38ecd74a24cb59da79181b95bfd3a是等比数列
C.若eqId93e38ecd74a24cb59da79181b95bfd3a是等差数列,则eqId1643644c71d94e83b60f42a9528e9d22
D.若eqId93e38ecd74a24cb59da79181b95bfd3a是等比数列,且eqId6a66565cb50049aa9ca1ffd617abe7a3eqIdcf86a3efea6a4f738de6634cd0fe6ad3,则eqId3bb9bc4cd01e42e2a99d52c54c58f62c
更新:2021/07/29组卷:131
单选题 | 较易(0.85) | 2021·全国高二专题练习
4 . 设eqIddd32472f6a6b463aaeabd7216b6ec52c,数列eqId2c1230a9ef5a4968be599681d676dd2b的前eqId5f904d1376ac4de7a7d6cfea92ff6981项和eqId90f8ea6e58864f3ebee8e62a6dd8ac27,则(   )
A.eqId2c1230a9ef5a4968be599681d676dd2b是等差数列B.eqId2c1230a9ef5a4968be599681d676dd2b是等比数列
C.当eqId018a236d12ae455085d17dcdc492e7e0时,eqIdc93d41bce614488fb12588cf61ea5246D.当eqId9f2905f51e334ad194ec2706ce6452a8时,eqId2979d99adc044814be30c58166d3e65f
解答题 | 一般(0.65) | 2021·辽宁
5 . 已知正项数列eqId93e38ecd74a24cb59da79181b95bfd3a的前eqId5f904d1376ac4de7a7d6cfea92ff6981项和为eqIddb5481de79c946c0a760143297d5eade,在①eqId2e19e0424ee34f2caac05c19df873f20;②eqIdcead12a814a941e7b55f5bf060c93ac6eqIda5665ef7f92b430ba697d0dbe2bb97a4;③eqId27f56a9f94434bf0a598e5051a0f1eedeqIde4efc197f90e4d3ab09e3b6b6db7df6deqId1bda9702379142f0bcdb7da757019421,这三个条件中选择一个作答.
(I)求数列eqId93e38ecd74a24cb59da79181b95bfd3a的通项公式;
(II)若数列eqIdeeb4ca98872f4e6d91cea28f43fc0b63的前eqId5f904d1376ac4de7a7d6cfea92ff6981项和为eqId92ed363a54bd4a8a93df9463bb3af1f5,且eqId7c07a1c0555641748e189344e4a69fd5,求证:eqId51a62f0e469a4736bcf13179a3d7c973
注:如果选择多个条件分别解答,按第一个解答计分.
解答题 | 较难(0.4) | 2022·全国高三专题练习
6 . 在①eqIde1fa8e9ee4b04f2db79e4807a869c2eb,②eqIda5fb9dfdd93544868a343480b2af435c,③eqIda21be162767b4a6ca74bf1fd65a60bdd这三个条件中任选一个,补充在下面问题中并作答.
已知数列eqId93e38ecd74a24cb59da79181b95bfd3a的各项均为正数,其前eqId5f904d1376ac4de7a7d6cfea92ff6981项和为eqIddb5481de79c946c0a760143297d5eade,且满足eqId43f51ea4f63c4ce596daefe4fbfa8f3f,________.
(1)证明:数列eqId93e38ecd74a24cb59da79181b95bfd3a是等差数列;
(2)若数列eqIdeeb4ca98872f4e6d91cea28f43fc0b63满足eqIdd85095493d7a422dba1a844fe067e937,其前eqId5f904d1376ac4de7a7d6cfea92ff6981项和为eqId92ed363a54bd4a8a93df9463bb3af1f5,且eqId54f05744e8eb4e2ebed0fcaf34c4661d对任意eqId7d4b353d04d64315b709fbb9768a1b60恒成立,求eqId75691f28a5bb4c8287401017aa3a2d29的取值范围.
注:如果选择多个条件分别解答,按第一个解答计分.
更新:2021/06/08组卷:230
单选题 | 较易(0.85) | 2021·全国
7 . 已知eqIddb5481de79c946c0a760143297d5eade是数列eqId93e38ecd74a24cb59da79181b95bfd3a的前eqId5f904d1376ac4de7a7d6cfea92ff6981项和,则“eqId1c9cfcf172214c96a3e5d4d9523e2c81”是“数列eqId93e38ecd74a24cb59da79181b95bfd3a是公差为2的等差数列”的(   )
A.充分不必要条件B.必要不充分条件
C.充要条件D.既不充分也不必要条件
8 . 设数列eqId93e38ecd74a24cb59da79181b95bfd3a的前eqId5f904d1376ac4de7a7d6cfea92ff6981项和eqIde1d393eeb81245088ea247630516fef8eqId0ce93bfa1f6a4a23b3258410dd19847a为常数),则下列命题中正确的是(   )
A.若eqId2c07a82215514a4eaf0b1325853b8f48,则eqId93e38ecd74a24cb59da79181b95bfd3a不是等差数列
B.若eqId0be4e678c13c4855b0d3f5c45188da09eqId5790ef4f0dda4f619edf362da41e0bc0eqId83852d75044b4ef6a65c857a110b59bb,则eqId93e38ecd74a24cb59da79181b95bfd3a是等差数列
C.若eqId0be4e678c13c4855b0d3f5c45188da09eqId5790ef4f0dda4f619edf362da41e0bc0eqId83852d75044b4ef6a65c857a110b59bb,则eqId93e38ecd74a24cb59da79181b95bfd3a是等比数列
D.若eqId316e2199840e418e87252dba1d7d7ffdeqIde28fbcee98794bd19b991981c6ed2721eqId05d3d028c5ed46ec956d14ef36cab36a,则eqId93e38ecd74a24cb59da79181b95bfd3a是等比数列
单选题 | 容易(0.94) | 2021·全国高三专题练习(理)
9 . 设eqIddb5481de79c946c0a760143297d5eade是数列eqId054d5a7de5684002909fe944c86227c2的前eqId5f904d1376ac4de7a7d6cfea92ff6981项和,若eqId1c7c130122b94c2aa5795591b3ae0226,则eqId39eb1fa6ddf244768efb605dc6dd050e(   ).
A.4043B.4042C.4041D.2021
填空题 | 较易(0.85) | 2020·全国(理)
10 . eqIddb5481de79c946c0a760143297d5eade为数列eqId2c1230a9ef5a4968be599681d676dd2b的前eqId92478644b29a4a0e8470a8c89d31b49f项和,若eqId57d06c11b76e428198afa670a7b12ff5,则eqId39f121ed471a4f75b6187dbf768cfc5b________.
更新:2021/01/05组卷:736