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解答题 | 较易(0.85) | 2021·全国高三其他模拟(理)
解题方法
1 . 已知等差数列eqId93e38ecd74a24cb59da79181b95bfd3a满足eqId8c6d99937cc248a18a1d3d62d30f98b3,正项等比数列eqIdeeb4ca98872f4e6d91cea28f43fc0b63满足首项为1,前3项和为7.
(1)求eqId93e38ecd74a24cb59da79181b95bfd3aeqIdeeb4ca98872f4e6d91cea28f43fc0b63的通项公式;
(2)求eqId180d24e3a5cc44ad938ce5290858e24d的前n项和eqIddb5481de79c946c0a760143297d5eade.
解答题 | 较易(0.85) | 2021·河北衡水市·高三其他模拟
2 . 在①eqIdcda14eff87534831bb4e826df93fc840,②eqId4925ac0270d0466f91edd98aecc99ec0,③eqId526579f05b6747fe8c3458c9e16ef471,这三个条件中任选一个,补充在下面的问题中,并解答该问题.
已知数列eqId7e042d6b38b14d879a8a54c4711921ba中,eqId1b870f8b46dc466aa4eb8cceaae660c7,满足___________,求数列eqId93e38ecd74a24cb59da79181b95bfd3a的前n项和eqIddb5481de79c946c0a760143297d5eade.
注:如果选择多个条件分别解答,按第一个解答计分.
解答题 | 一般(0.65) | 2021·全国高二专题练习
解题方法
3 . 数列{dn}满足,dneqIde557058046cb412e8a6ba1663a66b40a,求数列{dn}的前n项和Tn
更新:2021/06/14组卷:0
4 . 设数列eqId93e38ecd74a24cb59da79181b95bfd3a满足:eqId76c9975484ee44fa912426f342f70e07.设eqIddb5481de79c946c0a760143297d5eade为数列eqIdeeb4ca98872f4e6d91cea28f43fc0b63的前n项和,已知eqId9e7e06a5832a435083a671c86dbf5f25eqId65d68fc44eb24788b8a72242d8efd683
(1)求数列eqId93e38ecd74a24cb59da79181b95bfd3aeqIdeeb4ca98872f4e6d91cea28f43fc0b63的通项公式;
(2)设eqIdf2b71f1e0a6844d286e95fa5710dd709,求数列eqId74ef5fe5183946caaee41d8974816a20的前n项和eqId92ed363a54bd4a8a93df9463bb3af1f5
(3)证明:对任意eqId3e824472cf9f4d9bb0657a2101d2a534eqId10a29cfa29b242d2bf11f16d29380d81,有eqIddeca38e56d8441d28af5ed0a0e1657d8
5 . 已知递增等比数列eqId93e38ecd74a24cb59da79181b95bfd3a,和等差数列eqIdeeb4ca98872f4e6d91cea28f43fc0b63满足:eqIdef51378d6b3048fc94aece7f1b93e1afeqId46d68f4e66cf4136891c86d837a74e34,其中eqId2ed383b481084b888972df5aecf9b8f8,且eqId0509add794484602a2c710f41d9ddddceqId802dd8e915624120aa727fb9b14978b0eqId34a0e66a29434476be71839604577677的等差中项.
(1)求eqIdef9cef8e6d054d8dac46b8cde14953adeqId45a6b09a4fd24aecb1eafc7cf40bb354
(2)记数列eqId4d86b7dc6178422890a2a7995363abee的前n项和为eqId92ed363a54bd4a8a93df9463bb3af1f5,若当eqId532dc4d959024b79b546428f5856e5aa时,不等式eqId9bf9c25ff28b4f83a77dca9ef85a41b3,恒成立,求实数eqId5f420ef2d0b94c4b8a5d8e20a5d1ce2c取值范围.
解答题 | 一般(0.65) | 2021·重庆高三三模
解题方法
6 . 设等差数列eqId93e38ecd74a24cb59da79181b95bfd3a的前n项和为eqIddb5481de79c946c0a760143297d5eadeeqId89ff87418f52429b8e5d032d1f323bbaeqId5ee5d76b0541454081cbea39be9eb2cb.
(1)求eqIdef9cef8e6d054d8dac46b8cde14953ad
(2)若eqId89b0001393a24de3b083da5fc2c92e5ceqId92ed363a54bd4a8a93df9463bb3af1f5是数列eqIdeeb4ca98872f4e6d91cea28f43fc0b63的前n项和,求证:eqId03311aebd3ae4674a22874597e12b0c8.
解答题 | 一般(0.65) | 2021·四川自贡市·高三三模(理)
解题方法
7 . 已知数列{an}的前n项和为SneqId218f1c7b4af849dc92e3bef859d9d9ad,数列{bn}是等差数列,且b1=a1b6=a5.
(1)求数列{an}和{bn}的通项公式;
(2)若eqId1e78db1a6953470f9e27caa157778525,记数列{cn}的前n项和为Tn,证明:Tn<8.
双空题 | 一般(0.65) | 2021·全国高考真题
解题方法
8 . 某校学生在研究民间剪纸艺术时,发现剪纸时经常会沿纸的某条对称轴把纸对折,规格为eqId5cc3e0d583da41d5bd5b327352711aa3的长方形纸,对折1次共可以得到eqIddcf44ec65bb84025b2589d7625ce0bf6eqId6294a2118b0343e09983d22744d4cfd9两种规格的图形,它们的面积之和eqIdec331081d3504b008da50c715b8fc833,对折2次共可以得到eqId4cce79c4760f495eb325ba9a76020983eqId463b4ef06e1b481eb341a1f83f2c4d4beqId18950125728c4aa69f5d0b65a841b80d三种规格的图形,它们的面积之和eqIdc7245be90191412d88dd8fdf89986440,以此类推,则对折4次共可以得到不同规格图形的种数为______;如果对折eqId5f904d1376ac4de7a7d6cfea92ff6981次,那么eqId3f4601429abe4bf8b1e8486b3204596c______eqId9dfa48bde81644e38deeb2bed33ecfc6.
9 . 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
10 . 已知eqId93e38ecd74a24cb59da79181b95bfd3a是递增的等比数列,前eqId8898c1dc81824f3098bbeae74e8f11fd项和为eqId0bad15ca833c426894079a104ff88a36,且eqId90171c734cb448d989e3c49d55b37f4eeqId9561527b12364779bbc0aa025f8c3b19eqId82e5e0aaf6284e3ebbe74060f2cc3e3b成等差数列.
(1)求数列eqId93e38ecd74a24cb59da79181b95bfd3a的通项公式;
(2)各项均为正数的数列eqIdeeb4ca98872f4e6d91cea28f43fc0b63的首项eqId46d68f4e66cf4136891c86d837a74e34,其前eqId5f904d1376ac4de7a7d6cfea92ff6981项和为eqIddb5481de79c946c0a760143297d5eade,且______,若数列eqId74ef5fe5183946caaee41d8974816a20满足eqId88689d8c369e440cbc4f69290e69ec88,求eqId74ef5fe5183946caaee41d8974816a20的前eqId5f904d1376ac4de7a7d6cfea92ff6981项和eqId92ed363a54bd4a8a93df9463bb3af1f5.在如下三个条件中任意选择一个,填入上面横线处,并根据题意解决问题.①eqId6e7aefaa4e8c427bb62fc75567a5aa87;②eqId010a48e2ac434319be2dac2f7fd26354eqIdf763178cb35b499f81a4f8545aea37ee;③eqId562b3b3c894142ce90d15c800c13b28d.注:如果选择多个条件分别解答,按第一个解答计分.
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