组卷网>知识点选题>定义法判断等差数列
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1 . 已知eqId93e38ecd74a24cb59da79181b95bfd3a数列满足eqId1b870f8b46dc466aa4eb8cceaae660c7eqId8dbb1c8598794ced9056f8352291d438
(1)证明:数列eqId0af7de3c1a70443392076802cca01819为等差数列;
(2)求数列eqId65f736bf9e7441f8baaad09ec0a95165的前eqId5f904d1376ac4de7a7d6cfea92ff6981项和eqIddb5481de79c946c0a760143297d5eade
2 . 已知数列eqId93e38ecd74a24cb59da79181b95bfd3a的各项均为正数,记eqIddb5481de79c946c0a760143297d5eadeeqId93e38ecd74a24cb59da79181b95bfd3a的前n项和,从下面①②③中选取两个作为条件,证明另外一个成立.
①数列eqId93e38ecd74a24cb59da79181b95bfd3a是等差数列:②数列eqId950fed9c6fe44963948d9d4bfc8ce09a是等差数列;③eqId06afe02fc6d64f46a3a3c0998ba2c510
注:若选择不同的组合分别解答,则按第一个解答计分.
3 . 在数列eqId2c1230a9ef5a4968be599681d676dd2b中,若eqIde3dd17ca0a7345c29d2665f696b0bbf5eqIded444f319a744f1bb5232c54aac3c900.
(1)求证:数列eqId5c00b88f4b1440c49a23452d632f24b9是等差数列;
(2)求数列eqId2c1230a9ef5a4968be599681d676dd2b的通项公式eqIdef9cef8e6d054d8dac46b8cde14953ad及数列eqId0849af257a3c469a9e154cb67ee2bf3c的前n项和eqId92ed363a54bd4a8a93df9463bb3af1f5.
4 . 已知在数列eqId93e38ecd74a24cb59da79181b95bfd3a中,eqId681ee32b0980433e94ff5b7e029a5760eqId5e27ee47be584f0c8978d89ecbd1b517.
(1)求证:eqId93e38ecd74a24cb59da79181b95bfd3a为等差数列;
(2)设eqIdd04264b3bccb4fbc9b378efe0c1974dfeqId92ed363a54bd4a8a93df9463bb3af1f5为数列eqIdeeb4ca98872f4e6d91cea28f43fc0b63的前eqId92478644b29a4a0e8470a8c89d31b49f项和,求eqId92ed363a54bd4a8a93df9463bb3af1f5的最小值.
5 . 已知数列eqId93e38ecd74a24cb59da79181b95bfd3a的前eqId92478644b29a4a0e8470a8c89d31b49f项和为eqIddb5481de79c946c0a760143297d5eadeeqId77b3f6b9955e499dbdab033a38779496eqId5de640848aef4211adca74b68c925e2b,且eqIddded0887e994405db2034c27cf37e2df.
(1)求eqIdef9cef8e6d054d8dac46b8cde14953ad
(2)求证:eqId8be88eb26fb74b618cf59cd50affa183.
6 . 已知数列eqId93e38ecd74a24cb59da79181b95bfd3a中,eqId3a7e67c0d2084714b0eb508d75692427,且eqId44133afb8ff547449b28413c88310e8feqIdc052ddfbd4524f67a79e0e77c2e5656aeqIdef9cef8e6d054d8dac46b8cde14953adeqId3e824472cf9f4d9bb0657a2101d2a534)的等差中项.
(1)求数列eqId61920640dbc0439fb3d182ec901b821e的前eqId92478644b29a4a0e8470a8c89d31b49f项和eqIdc0e4a0296225411484470eabe7dc0c79
(2)设eqId19499a7bf8e54d1ebf0064d96d6633c2,判断数列eqId46dd7fd51146439da45fc5731c33333c是否存在最大项和最小项?若存在求出,不存在说明理由.
解答题 | 一般(0.65) | 2021·上海市建平中学高三三模
7 . 已知无穷数列eqId93e38ecd74a24cb59da79181b95bfd3a,对于任意给定的正整数eqId69f56ef2c88b4b73a560da59f5247a82,设不等式eqId7c3d43d8aadc45629d698c763824fe91对任意eqId7d4b353d04d64315b709fbb9768a1b60恒成立时eqId414507d4b929493caac150498e13d888的取值集合为eqId2198caa755ec49c887f4a8ed6f9e967b.
(1)eqId245c4552fa804098945b4a058d99449a,求集合eqIdbbfcf11cfdb64e33a851d87edbc70c6c
(2)若eqId93e38ecd74a24cb59da79181b95bfd3a为等差数列,公差为eqId0beafc0779aa41fdb343d52e98143a82,求eqId2198caa755ec49c887f4a8ed6f9e967b
(3)若对任意eqIdd4aaa0c114574153935f6c7efb01e278eqId7b442cd0f37a4a8e98efc22e695a16ddeqId2198caa755ec49c887f4a8ed6f9e967b均为相同的单元素集合,证明:数列eqId93e38ecd74a24cb59da79181b95bfd3a为等差数列.
8 . 数列eqId93e38ecd74a24cb59da79181b95bfd3a满足:eqId592a46b984e0424096d7d0aac714160b,且对任意eqId6c2146ec6df54fc9af9b2aef04489c8b,都有eqId86d94189b643426fa3237cd1721b0c9b
(1)求eqId45a5c001871545d0913be31306c783d2
(2)设eqId60df3eb9aa59466ba15fe468240151e9,求证:对任意eqId6c2146ec6df54fc9af9b2aef04489c8b,都有eqIdadcd3af3b24b45e7a95e611ad3f343b3
(3)求数列eqId93e38ecd74a24cb59da79181b95bfd3a的通项公式eqIdef9cef8e6d054d8dac46b8cde14953ad
9 . 已知数列eqId93e38ecd74a24cb59da79181b95bfd3an项和为eqIddb5481de79c946c0a760143297d5eade,数列eqId021774d0d89b4969b5b322899f41ac3c是以1为首项,1为公差的等差数列,则eqId87464dfb5fe64cf78aad6604318bcfb9的最大值是________
10 . 已知数列eqId2c1230a9ef5a4968be599681d676dd2b是等比数列,且公比eqIda5d0fc594d4048549d5bbda484fbecc8不等于1,eqId93044fb35772443483c4cf65cef05c63,数列eqIda0db2906046940e19de8782f94f34137满足eqId23a014540b8543c3842c4dcf331c14b4.
(1)求证:数列eqIda0db2906046940e19de8782f94f34137是等差数列;
(2)求数列eqId0d0e7e35b6a24678a8083bc79ade0d45的前eqId92478644b29a4a0e8470a8c89d31b49f项和eqIddb5481de79c946c0a760143297d5eade.
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