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1 . 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
2 . 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.
3 . 已知数列eqId93e38ecd74a24cb59da79181b95bfd3a满足:eqIda5abe620e67e45aa924145e9cf183f10eqId076699cd73764709b1f170e71ee4c29d,数列eqIdeeb4ca98872f4e6d91cea28f43fc0b63满足:eqId46d68f4e66cf4136891c86d837a74e34eqIdb8907da2a153460fba1e450649c355fd,求证:eqId20873cd5f824425686bd5d2aea1ed558
4 . 已知数列eqId054d5a7de5684002909fe944c86227c2的前n项和为eqIddb5481de79c946c0a760143297d5eade,且满足eqId331aa876f7f741e6be239ca7574883bc,数列eqId69fa66742e6b480eb0e55f574b8b7749的通项eqIdf25a6d5c7fea411e9d17d1db45f8885c,则使得eqIdc44b55f713624976876d7f4662bda372恒成立的最小的k值最接近(   )
A.eqId49b7b111d23b44a9990c2312dc3b7ed9B.eqId5255aa721623485f9dfbfd166a59c97aC.eqId44aff622a095465082b61837e24439e7D.1
5 . 设eqIddb5481de79c946c0a760143297d5eade为数列eqId93e38ecd74a24cb59da79181b95bfd3a的前eqId5f904d1376ac4de7a7d6cfea92ff6981项和,满足eqIdb319000f94614f2eb29e7068e7505b1beqIdf66b9325b0c94f8eabb20ab49bb8fabf,其中eqId532dc4d959024b79b546428f5856e5aa,数列eqId92e48c32f97b440ca0cff79e8a1436ef的前eqId5f904d1376ac4de7a7d6cfea92ff6981项和为eqId92ed363a54bd4a8a93df9463bb3af1f5,则eqIda8299116019f4c5883735438417e034c___________.
解答题 | 一般(0.65) | 2021·全国高三专题练习
6 . 已知函数eqId7562b4a6351c4278bbc2cf45b99b135beqIde7cdba499a9c499aa0e351616a859d31,证明:eqId8e2503e9ad604a5aa73517ffe44552b5,其中,eqId075d44d1e421488b950d298144815f07
解答题 | 一般(0.65) | 2021·全国高三专题练习
7 . 已知数列eqId93e38ecd74a24cb59da79181b95bfd3aeqIdd4a8b178447846e5979f7965a2428bd5,是否存在正数k,使对一切eqId532dc4d959024b79b546428f5856e5aa,不等式eqId0d904d6d1f0a4367ba0224aaab6aa040均成立?
8 . 设等比数列eqId93e38ecd74a24cb59da79181b95bfd3aeqId2bde4aed9c474f8b99fdeba8d1c71fc1)的前n项和为eqIddb5481de79c946c0a760143297d5eade,且eqIdfb0fafaf99bd4b03bbdcd3fa4c8e5d40,其中a是不为零的常数.
(1)eqId278f4a80fb99455dbf9354b008329213时,求数列eqId93e38ecd74a24cb59da79181b95bfd3a的通项公式;
(2)在(1)的条件下,若数列eqIdeeb4ca98872f4e6d91cea28f43fc0b63eqId2bde4aed9c474f8b99fdeba8d1c71fc1)满足eqIdd6594a6bb8824d33bc0b7cf8233749deeqId2bde4aed9c474f8b99fdeba8d1c71fc1),eqId332298991ed249c2a9933965bc84ff56,求数列eqIdeeb4ca98872f4e6d91cea28f43fc0b63eqId2bde4aed9c474f8b99fdeba8d1c71fc1)的通项公式.
解答题 | 一般(0.65) | 2021·全国高三专题练习
9 . 已知数列eqId93e38ecd74a24cb59da79181b95bfd3a中,eqId8f8f31c3a14f4ed5ac209a602b672106,当n取何值时,eqId4224c303ef854035b455fe10223f984f取得最值?
解答题 | 一般(0.65) | 2021·全国高三专题练习
10 . 已知eqIda0833835dc7c4c6faaf105151795d786eqIdb6954fbabc004aa0950f6e0287774187eqId2bde4aed9c474f8b99fdeba8d1c71fc1,且eqId9524686794bb48bda77837cbe6ec04c8
(1)当eqIda306861baef14039b8f8065f4866764a时,求证:eqId3e3926c8a0e34718bead12a9c327b424
(2)试确定一个正整数eqIdf9dc02c0e76840379a3469b130aad5f0,使得当eqIddd0607f9919240e6b75997fcbe77de66时,都有eqId7a523919e52c4faeba8d8f8263a865f4