组卷网>知识点选题>第六章 数列
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解答题 | 困难(0.15) | 2021·全国高三专题练习
解题方法
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1 . 如图所示,eqId932dc4d9c7184c24aab5114be741a1d8eqId2e17381e688541cfadc3d16cfaa43930,…,eqId263cdd8cb10849fabe410ed2d1dfb972,…是曲线eqIdfd71c38c03bd4dee94182878b9d14ebdeqId020b3bfabcc447eb9dd3745015e9610f)上的点,eqIdcdd564f687b0411283dda6953b7078c4eqId56612a62b4864f77866e5d5380b54a43,…,eqIdb98f4e0a87354db29b319100e6c2f278,…是x轴正半轴上的点,且eqIdc42529176a294f5390db813c3d4116c3eqId3f5357826cf346e4ba586d4f46595c34,…,eqIdc77ceb0ee0d246038486a532da540956,…均为等腰直角三角形(eqId2ad0f64a49ee42e1b10924a6973900d2为坐标原点).
说明: figure
(1)求数列eqId93e38ecd74a24cb59da79181b95bfd3a的通项公式;
(2)设eqId0b360e399f2d4683a936e0864026160a,求eqIddb5481de79c946c0a760143297d5eade.
解答题 | 一般(0.65) | 2021·邵东市第一中学高三月考
解题方法
2 . 设各项均为正数的数列eqId93e38ecd74a24cb59da79181b95bfd3a的前eqId5f904d1376ac4de7a7d6cfea92ff6981项和为eqIddb5481de79c946c0a760143297d5eade,若eqIdeb0397580b5c4ec5b9fa8c323bfdde77构成等比数列,且eqIdc6414d2cbc4849bd94b876e88aa56d80
(1)求数列eqId93e38ecd74a24cb59da79181b95bfd3a的通项公式;
(2)求证:对任意正整数eqId5f904d1376ac4de7a7d6cfea92ff6981,有eqIdd1231ecd3eb842909b807db868c5a74e
解答题 | 一般(0.65) | 2021·全国高三专题练习
解题方法
3 . 已知eqIdc2d3271b09324d98954c33293515c0e9eqId996cba1180c54a3cb1dde3bc15758c29eqIdffdb22cbc9ab4fa9866f2b4b21a11eb3.求证:eqIdc7638c88b56b4c77ae629fe2b88e4e7a,其中eqId532dc4d959024b79b546428f5856e5aa
解答题 | 一般(0.65) | 2021·全国高三专题练习
4 . 设F是椭圆eqId27db313f47174b4c9e841384e7304ec4的右焦点,且椭圆上至少有21个不同的点eqId9f50f48e8d0e4db981b17ac1190b6127eqId4dbcf768f0d64d188031f05c52d11601,2,…),使eqId8c40a625bdc64f52a8a6affe12d3a3eceqIdbda5a8d0b96f4599b5b046a04c2c5d0feqId5d0076eb0e9b4f1d9287e97b4731217a,…组成公差为d的等差数列,求a的取值范围.
5 . 已知等差数列eqId93e38ecd74a24cb59da79181b95bfd3a的前eqId5f904d1376ac4de7a7d6cfea92ff6981项和为eqIddb5481de79c946c0a760143297d5eadeeqIdc1e4d301eec54450bd5d8b768691ec82eqIdc5d5e188223c4dd2815ee6355e0c41ad,数列eqIdeeb4ca98872f4e6d91cea28f43fc0b63的前eqId5f904d1376ac4de7a7d6cfea92ff6981项和eqIdbbd89869dc2f482dbf7ae9d0f2befc94
(1)求数列eqId93e38ecd74a24cb59da79181b95bfd3aeqIdeeb4ca98872f4e6d91cea28f43fc0b63的通项公式;
(2)若数列eqId74ef5fe5183946caaee41d8974816a20满足eqIdc1aa5662afa347e582efda825bf46eef,求数列eqId74ef5fe5183946caaee41d8974816a20的前eqId5f904d1376ac4de7a7d6cfea92ff6981项和eqIdb10e0852b5ff41eabe1836f73d97391a
解答题 | 较难(0.4) | 2021·全国高三专题练习
6 . 已知函数eqId6f13759e937144069819aed2ae5a1057与函数eqIdd85d65356ca343c483d54afc7218f91a的图像关于直线eqIdf4cf79cbbea14d298940773ea43ed467对称,
(1)在数列eqId93e38ecd74a24cb59da79181b95bfd3a中,eqIdc2d3271b09324d98954c33293515c0e9,当eqIda306861baef14039b8f8065f4866764a时,eqIdfd20672d968b4827a60041cc6cb4a22e,在数列eqIdeeb4ca98872f4e6d91cea28f43fc0b63中,eqId332298991ed249c2a9933965bc84ff56eqIdb9d70c2ed9cd4962abb7e8974b6be6b2,若点eqIdc61448ea13b549c398163e109957cd6b在函数eqId6f13759e937144069819aed2ae5a1057的图像上,求a的值.
(2)在(1)的条件下,过点eqIdb10e0852b5ff41eabe1836f73d97391a作倾斜角为eqId9e7f9209cee04cdb9a06395310730b31的直线eqId66f3d767f2ee47f48d033cee6802640a,若eqId66f3d767f2ee47f48d033cee6802640ay轴上的截距为eqId2284627aba2c4400920eb246dfa9e0b1,求数列eqId93e38ecd74a24cb59da79181b95bfd3a的通项公式.
7 . (1)已知数列eqId50623a2ce8b5456c9d012c2d2d27c438,其中eqIde7fa766ad970441190913eb77bb92ee1,且数列eqIdb3e3b364e9f84387b06e79193f2a39cc为等比数列,求常数P
(2)设函数eqId4d3e93a6d87549de932f2ff7ade9eadb定义域为R,当eqId4db620a5946b4ee0a9f530f35a6d505a时,eqId4157df7d4b044f62862a09a132e9f439,且对于任意的xeqIda96c35333bce498fac43d585fdcaf8c2,有eqIdd3f90a1b9d6f4ce4bf28b92bf498b748成立,数列eqId054d5a7de5684002909fe944c86227c2满足eqId84af6848c7dd45b78800f79aa0dba4c5,且eqId00f664fc2db342bca09b48d9e612fbffeqId6c2146ec6df54fc9af9b2aef04489c8b).求数列eqId054d5a7de5684002909fe944c86227c2的通项公式并证明.
8 . 已知数集eqId60213abfc04f41f194b54e1b5477e0ddeqIdf5eed1a9e59943bf96fda0aaa04505da具有性质eqIdbedf755e0fdb4d078d6859360706b163;对任意的eqIdb6e15e51d29a47a7aff44f98b1aafaeeeqIdc7d58dd623df4bdab3285964173faf12eqId65789af189094617be07e8fb774c53a1eqIde622433bd0b845a98f3e875663085dadeqId21561b9a85f84b8095b5f7dd321fcff9两数中至少有一个属于eqId052844cae8574a8ab842c38a039baac0
(1)分别判断数集eqId5a881c0516d4418ca2465111f74c1261eqId4dac061e530c453d99d23493a98c8463是否具有性质eqIdbedf755e0fdb4d078d6859360706b163,并说明理由;
(2)证明:eqIdc2d3271b09324d98954c33293515c0e9,且eqIdbc1b6c224c4143aebd364e6d64454282
(3)证明:当eqIdf6349457aaf947d383f925cd9bb53620时,eqIdb5a0ee5591bb4364a22da1c2218e7bfceqId2c08dbf3fb4c466caaa6d6230082794ceqId5cae532f2168495188622189ec8df62ceqId310274b5ffe34ad58a069683d0dac787eqIdd80748a60dc04eb5bc4556d4e5cad370成等比数列.
9 . 数列eqId2c1230a9ef5a4968be599681d676dd2b中,“eqId73b01961a2cc4c188215a326eff77a80eqIdc25184d2b1c04a7fab041fa24fbd5907”是“eqId2c1230a9ef5a4968be599681d676dd2b是公比为2的等比数列”的(   )
A.充分而不必要条件B.必要而不充分条件
C.充分必要条件D.既不充分也不必要条件
解答题 | 一般(0.65) | 2021·全国高三专题练习
解题方法
10 . 已知函数eqId1ce2415e9ddb4ded8b31462e07f0784feqId0eda43edeae142b3be2a2d09274bd73e,数列eqId93e38ecd74a24cb59da79181b95bfd3a是各项均不为0的等差数列,点eqId94998a6e896842bcbb042d153b175737在函数eqId10852d81bc184140a7780250c82c6929的图像上,数列eqIdeeb4ca98872f4e6d91cea28f43fc0b63满足eqId332298991ed249c2a9933965bc84ff56eqId7b03d05afdeb484abe2b6d15d06efdc4,且eqId69601cc2522f46828e8bcf66f59d8426eqId6c2146ec6df54fc9af9b2aef04489c8b),
(1)求数列eqId93e38ecd74a24cb59da79181b95bfd3a的通项公式,并证明数列eqId9a27190e96f4457585dc495bf191eee4是等比数列;
(2)若数列eqId74ef5fe5183946caaee41d8974816a20满足eqIdc9bbf622af9e491880a83600a4269702,求证:eqId8cbfcab0fb7a46d29980948c1b230471