组卷网>知识点选题>等差数列
显示知识点
显示答案
| 共计 1201 道试题
1 . (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.
多选题 | 一般(0.65) | 2022·全国高三专题练习
2 . 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 | 一般(0.65) | 2021·全国高三专题练习
3 . 已知等差数列eqId93e38ecd74a24cb59da79181b95bfd3a及关于x的方程eqIdf3ba45abda804d45a499bf5c4e9d3630eqId6c2146ec6df54fc9af9b2aef04489c8b),且数列eqId93e38ecd74a24cb59da79181b95bfd3a的公差eqIdb2d67ea9304442eabd5ba21bd2c29656
(1)求证:这些方程有一个公共根;
(2)若方程的另一根为eqId0926f6c8f74748d784074f0759f0f374,求证:数列eqId86af9f628a6447be9236fe8604077e68为等差数列;
(3)若数列eqId93e38ecd74a24cb59da79181b95bfd3a的任意两不同项eqId89f245dd67f34e3093c65087a95ebf21eqIdc77e21a2202c4d319cc4701057e06642meqId27bfb574b99843489812199e3f44cd5c)之和都是数列eqId93e38ecd74a24cb59da79181b95bfd3a的项,求eqIdb5a0ee5591bb4364a22da1c2218e7bfcd满足的充要条件.
6 . 数列eqId93e38ecd74a24cb59da79181b95bfd3a中,eqId5de640848aef4211adca74b68c925e2beqIde1d6601e182e4d18b5ed7b899a6cbf36,其中eqIddb5481de79c946c0a760143297d5eadeeqId93e38ecd74a24cb59da79181b95bfd3a的前eqId5f904d1376ac4de7a7d6cfea92ff6981项和.
(1)求eqId93e38ecd74a24cb59da79181b95bfd3a的通项公式;
(2)证明:eqIde87c0f9b05044dd29ac6627503de170e.
7 . 已知数列eqId93e38ecd74a24cb59da79181b95bfd3a满足eqIdc2d3271b09324d98954c33293515c0e9eqId1af4a7b554104101b4ee305a7afb393b,且eqId30a55104a2d54fa0a0ef1b16ffb98855=eqIdc21520925e1943d7815d36d5295c366a+eqId743d1abe0bcb43abbca820ed1695f0cf-eqId9e9fc94f50d143cbb30d094931989550n≥2),则数列eqId93e38ecd74a24cb59da79181b95bfd3a的通项公式为_____________.
8 . 已知数列eqId3c18fbe2d7494c549205a6355581345a满足eqId555139d2b3e24e968402f9a17062b86deqIdce0f2fa82f5c4a748beb1afdd451163a,设eqIda270eb30196d4182bc6d22624e58afff.
(I)证明:eqIdeeb4ca98872f4e6d91cea28f43fc0b63为等差数列;
(II)设eqId9393110e73264e70a0924c672cea5bd4,若eqId558c17324d4f40c8b990a5f077e40f0c为递增数列,求eqId5f420ef2d0b94c4b8a5d8e20a5d1ce2c的取值范围.
10 . 在等差数列{an}中,a1+a3+a5=105,a2+a4+a6=99,以Sn表示{an}的前n项和,则使Sn达到最大值的n___________.