组卷网>知识点选题>函数单调性法求等差数列前n项和的最值
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1 . 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___________.
2 . 设eqIddb5481de79c946c0a760143297d5eade是等差数列eqId93e38ecd74a24cb59da79181b95bfd3a的前eqId5f904d1376ac4de7a7d6cfea92ff6981项和,eqId21ad4ded655f4be08767e73cf9623e3f,______.
从①eqId7d3e63821e824cd7909bd6ddb4ae6ace,②eqIda6fd5089083b416ca63cdca937783c70,③eqIde3bc0e3362eb401a9a5a6a8c4d806c10中任选一个条件,补充在上面的横线上,并回答下列问题.
(1)求数列eqId93e38ecd74a24cb59da79181b95bfd3a的通项公式;
(2)求数列eqId93e38ecd74a24cb59da79181b95bfd3a的前eqId5f904d1376ac4de7a7d6cfea92ff6981项和eqIddb5481de79c946c0a760143297d5eade的最值.
3 . 若数列eqId054d5a7de5684002909fe944c86227c2是等差数列,首项eqId6a66565cb50049aa9ca1ffd617abe7a3,公差eqId4a0d8dfddeab4ce28ae5f32483bea9d8,且eqId1e8690bcef5340849dead5930fbd5f92eqId0ba40c0a4f714d25b8c222625d9b639f,则使数列eqId054d5a7de5684002909fe944c86227c2的前eqId5f904d1376ac4de7a7d6cfea92ff6981项和eqId95b8c8174b054abe8d11e9a5299312b1成立的最大自然数eqId5f904d1376ac4de7a7d6cfea92ff6981是(   )
A.4039B.4038C.4037D.4036
5 . 已知等差数列eqId93e38ecd74a24cb59da79181b95bfd3a的前eqId5f904d1376ac4de7a7d6cfea92ff6981项和为eqIddb5481de79c946c0a760143297d5eadeeqId6a66565cb50049aa9ca1ffd617abe7a3,公差eqId4a0d8dfddeab4ce28ae5f32483bea9d8eqId2c07a1eabc4440ddaa8809bc9b701d2b.若eqIddb5481de79c946c0a760143297d5eade取得最大值,则eqId8c4243d3a68d483db73d7f4203c7e940________
6 . 已知数列eqId93e38ecd74a24cb59da79181b95bfd3a的前eqId5f904d1376ac4de7a7d6cfea92ff6981项和eqIddb5481de79c946c0a760143297d5eade满足eqId7ec08710fac242008bd80bc82b271c5b,且eqId8c7c4b8d2cd5414d80d1cedee8ba88a6.
(1)求eqIdb5a0ee5591bb4364a22da1c2218e7bfceqId2c08dbf3fb4c466caaa6d6230082794c
(2)求eqId93e38ecd74a24cb59da79181b95bfd3a的通项公式;
(3)令eqId6e5d5acd17c649268aa7f81225664c8b,求数列eqIdeeb4ca98872f4e6d91cea28f43fc0b63的前eqId5f904d1376ac4de7a7d6cfea92ff6981项和eqId92ed363a54bd4a8a93df9463bb3af1f5的最大值.
7 . 设数列eqId93e38ecd74a24cb59da79181b95bfd3a是以eqId0beafc0779aa41fdb343d52e98143a82为公差的等差数列,eqIddb5481de79c946c0a760143297d5eade是其前eqId5f904d1376ac4de7a7d6cfea92ff6981项和,eqId6a66565cb50049aa9ca1ffd617abe7a3,且eqIdc8a885cdbd1d47f6830868b9a35d7167,则下列结论正确的是(   )
A.eqId4a0d8dfddeab4ce28ae5f32483bea9d8B.eqId38b40422878e4422a4e0f197c0fe74edC.eqId25f0ec67183948bdbf48eca708ce36cdD.eqId66323e1f327444beacb68797109eb651eqIdb4de3265b5d64840ad8080068acf2dadeqIddb5481de79c946c0a760143297d5eade的最小值
8 . 已知数列eqId93e38ecd74a24cb59da79181b95bfd3a的前eqId5f904d1376ac4de7a7d6cfea92ff6981项和为eqId9edb4b521a364a449d3fae387ebb2564,则下列说法正确的是(   )
A.eqId63f9bda3f67c4f60bd949c6cabc3801cB.eqId9640e0e6b9264c85b390133bcd4b4ba8eqIddb5481de79c946c0a760143297d5eade的最小值
C.eqIdc94a19e338924e51b34579bcfada8ddaD.使得eqId95b8c8174b054abe8d11e9a5299312b1成立的eqId5f904d1376ac4de7a7d6cfea92ff6981的最大值为33
9 . 在等差数列eqId2c1230a9ef5a4968be599681d676dd2b中,其前eqId5f904d1376ac4de7a7d6cfea92ff6981的和是eqIddb5481de79c946c0a760143297d5eade,若eqId3a7e67c0d2084714b0eb508d75692427eqId87866bd0fe4a466d8875b91c6792486e,则(   )
A.eqId2c1230a9ef5a4968be599681d676dd2b是递增数列B.其通项公式是eqIdefcb16d21ad74c94aa778606a0bc1dae
C.当eqIddb5481de79c946c0a760143297d5eade取最小值时,eqId5f904d1376ac4de7a7d6cfea92ff6981的值只能是eqId8898c1dc81824f3098bbeae74e8f11fdD.eqIddb5481de79c946c0a760143297d5eade的最小值是eqIdd1342446cf284d02aeace61cd8688be8
10 . 设eqId93e38ecd74a24cb59da79181b95bfd3a是等差数列,eqIdd239b91136cc4831854bd016b0df0192,且eqId509efc87f2454020935e82662fdc279aeqId683230e35330405a88f28a55246a18a9eqId2f357fc7f2f342ce93ec29a68ab5d4b3成等比数列.
(1)求eqId93e38ecd74a24cb59da79181b95bfd3a的通项公式.
(2)记eqId93e38ecd74a24cb59da79181b95bfd3a的前eqId5f904d1376ac4de7a7d6cfea92ff6981项和为eqIddb5481de79c946c0a760143297d5eade,求eqIddb5481de79c946c0a760143297d5eade的最小值.
(3)记eqId61920640dbc0439fb3d182ec901b821e的前eqId5f904d1376ac4de7a7d6cfea92ff6981项和为eqId92ed363a54bd4a8a93df9463bb3af1f5,求eqId92ed363a54bd4a8a93df9463bb3af1f5的表达式.