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1 . 已知等比数列
满足
,,则
的值为( )
![](/uploads/image/squformula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](/uploads/image/squformula/3299d1d394efc1381671b1632e6e87e1.png)
![](/uploads/image/squformula/daf464629fa321a6ff7401ab79f07083.png)
a.![]() | b.![]() |
c.![]() | d.![]() |
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解题方法
2 . 已知数列
的前
项和为
,
.
(1)若
是等比数列且公比
,求
;
(2)若
是等差数列且
,求
的最小值.
![](/uploads/image/squformula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](/uploads/image/squformula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](/uploads/image/squformula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](/uploads/image/squformula/21f658ddec0caf5c5904e4e6ccbba7a6.png)
(1)若
![](/uploads/image/squformula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](/uploads/image/squformula/2f5b78d8869e45eb2baf7422155a0992.png)
![](/uploads/image/squformula/6c1ccc6c74b8754e9bcbb3f39a11b6f1.png)
(2)若
![](/uploads/image/squformula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](/uploads/image/squformula/738dc67ac3b150252a964d1ffe3dfa63.png)
![](/uploads/image/squformula/08eb71ecf8d733b6932f4680874dbbf3.png)
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3 . 在高层建筑中,为了优化建筑结构,减少风荷载影响,设计师可能会将建筑设计成底面楼层高度比较高,随着楼层往上逐步按照等比数列递减的“金字塔”形状,已知某高层建筑共10层,第2层高度为
,第
层高度记为
,
是公比为的等比数列,若第层高度小于
,则的最小值为( )
![](/uploads/image/squformula/8fc48ba42c557fcece260522b3c10952.png)
![](/uploads/image/squformula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](/uploads/image/squformula/80664ade8b4f3c97f8ca354dae9030b7.png)
![](/uploads/image/squformula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](/uploads/image/squformula/9e17ee14bd91bfff409c06fd434f6745.png)
a.6 | b.5 | c.4 | d.3 |
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4 . 已知数列
是等差数列,数列
是正项等比数列,且
,
,
是和
的等差中项,
是
和
的等比中项.
(1)求数列
和数列
的通项公式;
(2)令
,求数列
的前n项和.
![](/uploads/image/squformula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](/uploads/image/squformula/034ba25825c13725931c483aa47c9363.png)
![](/uploads/image/squformula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](/uploads/image/squformula/2a0d29f34218cd60cc6e9ce4dcd13925.png)
![](/uploads/image/squformula/b715e7842b95f654f16056a7c7f2abe9.png)
![](/uploads/image/squformula/6c1ccc6c74b8754e9bcbb3f39a11b6f1.png)
![](/uploads/image/squformula/f65fc200f10b97588a0c9896277c9c64.png)
![](/uploads/image/squformula/b715e7842b95f654f16056a7c7f2abe9.png)
![](/uploads/image/squformula/57483e04fd1840c87ac5325157149877.png)
(1)求数列
![](/uploads/image/squformula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](/uploads/image/squformula/034ba25825c13725931c483aa47c9363.png)
(2)令
![](/uploads/image/squformula/115f794e70a18315fb41bdbbb599eb5b.png)
![](/uploads/image/squformula/57ef6d44448092ebdb9e4a49d866a749.png)
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5 . 等比数列
中,,则
为( )
![](/uploads/image/squformula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](/uploads/image/squformula/daf464629fa321a6ff7401ab79f07083.png)
a.2 | b.4 | c.8 | d.16 |
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6 . 已知数列
的前
项和
满足
,且
成等差数列,则![](/uploads/image/squformula/7999465d0e871febde66296a0cbf058c.png)
__________ ;![](/uploads/image/squformula/e3f7fda69e2b32b9ced2239f915fa59b.png)
__________ .
![](/uploads/image/squformula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](/uploads/image/squformula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](/uploads/image/squformula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](/uploads/image/squformula/f16fe3ffe7d9e8246282ddb00fc5f4b2.png)
![](/uploads/image/squformula/d6cedd84e3f080e5931a490644149f30.png)
![](/uploads/image/squformula/7999465d0e871febde66296a0cbf058c.png)
![](/uploads/image/squformula/e3f7fda69e2b32b9ced2239f915fa59b.png)
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名校
解题方法
7 . 在等比数列
中.
(1)已知
,
,求前4项和
;
(2)已知公比
,前6项和
,求.
![](/uploads/image/squformula/83cf38189d5cbf627d2b82ac0eb76006.png)
(1)已知
![](/uploads/image/squformula/2815b24f5a89be7ae53aed93182e8988.png)
![](/uploads/image/squformula/ea432be66a5d2f9c5198ff656b18fd32.png)
![](/uploads/image/squformula/0f30f56664446f32dbbc2c5f12a99374.png)
(2)已知公比
![](/uploads/image/squformula/26d9b6c86435e0ceff94d8ad1cd03737.png)
![](/uploads/image/squformula/a8b7b67a73a815fb9792f0567396a78b.png)
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8 . 已知数列
是等差数列,满足
,
,数列
是首项为1的等比数列,且
,
,
成等差数列.
(1)求
,
的通项公式;
(2)设
,求数列
的前
项和.
![](/uploads/image/squformula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](/uploads/image/squformula/be0d1a492ec22f4ca2372e2c59c61d6c.png)
![](/uploads/image/squformula/79b50b3927041221a53f19b6a0549d71.png)
![](/uploads/image/squformula/034ba25825c13725931c483aa47c9363.png)
![](/uploads/image/squformula/d0eeacc31bfbd4c536bb52bbaec43dd3.png)
![](/uploads/image/squformula/1a8aada7b854c906305d0747c33f9929.png)
![](/uploads/image/squformula/57483e04fd1840c87ac5325157149877.png)
(1)求
![](/uploads/image/squformula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](/uploads/image/squformula/034ba25825c13725931c483aa47c9363.png)
(2)设
![](/uploads/image/squformula/1d44ddab6e0c60119be69985ae7fa65b.png)
![](/uploads/image/squformula/57ef6d44448092ebdb9e4a49d866a749.png)
![](/uploads/image/squformula/b6a24198bd04c29321ae5dc5a28fe421.png)
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9 . 已知数列
为等比数列,
,
,则![](/uploads/image/squformula/b08a8c9baca410ef1464caf7f522aa4a.png)
______ .
![](/uploads/image/squformula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](/uploads/image/squformula/25fc6e4698a74a39097e891812c976ae.png)
![](/uploads/image/squformula/8f9cd956a1474fbd54dc49f2ad77d9a0.png)
![](/uploads/image/squformula/b08a8c9baca410ef1464caf7f522aa4a.png)
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解题方法
10 . 设
是等差数列,
是等比数列,公比大于0,已知
,
,
,
.
(1)求数列
和
的通项公式:
(2)设
,求数列
的前n项和
.
![](/uploads/image/squformula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](/uploads/image/squformula/0f329b217e1051b23f0d61023cdc6e69.png)
![](/uploads/image/squformula/85444874c705666de9488286d3d61dd1.png)
![](/uploads/image/squformula/b5c340fdadffa2f9120a70430ce477f8.png)
![](/uploads/image/squformula/66f3c8fbfb3610705619193ee6e77d5d.png)
![](/uploads/image/squformula/00a5a59be5dbb975e898afe484ccafec.png)
(1)求数列
![](/uploads/image/squformula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](/uploads/image/squformula/0f329b217e1051b23f0d61023cdc6e69.png)
(2)设
![](/uploads/image/squformula/ac07953530e3c248b3438fb200fb1661.png)
![](/uploads/image/squformula/c5ab0309e2cd35585ea9fb2cc3017abf.png)
![](/uploads/image/squformula/08eb71ecf8d733b6932f4680874dbbf3.png)
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