1 . 已知正项等比数列
的前3项和为26,且数列
的前3项和为
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af9bbe98100c8067ff36ac536d043a85.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41cf1da18d91f7c98086553d157d1a87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ed687b5e72317b508124642dd043d32.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af9bbe98100c8067ff36ac536d043a85.png)
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2024-02-17更新
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3卷引用:甘肃省武威市凉州区2023-2024学年高二下学期开校质量检测数学试卷
甘肃省武威市凉州区2023-2024学年高二下学期开校质量检测数学试卷(已下线)专题03等比数列及其前n项和6种常考题型归类【好题汇编】-备战2023-2024学年高二数学下学期期末真题分类汇编(北师大版2019选择性必修第二册)河南省驻马店市2023-2024学年高三上学期期末统一考试数学试题
解题方法
2 . 等比数列
的前
项和为
,下列结论正确的是__________ (填序号).
①若
,公比为
,则
;
②数列
一定是等比数列;
③数列
一定是等比数列;
④对任意正整数
;
⑤数列
一定是等比数列.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
①若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94351ce858fa3f3a09cfadc2d23d7253.png)
②数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e3550967afc46107173c1c3b8acdc53.png)
③数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b00dd05f91430b9a89e62beed9499919.png)
④对任意正整数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e57ff738a95729d7b526386b0ad323c2.png)
⑤数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52d9f7e125f35a2953bead1c36313bd2.png)
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3 . 在公比为
的等比数列
中,
为其前
项和,
(
),且
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad0d99fef1aa4dbcc6dc7b30b7d2c9a9.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47d9b426bcc34a2cca2184dc1310f5e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fec0f03c8c144f76d8528e91f16bf273.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ecc950c9a303865d535fa7883bad432b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4720821a9360798a78a61c08be4f28ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad0d99fef1aa4dbcc6dc7b30b7d2c9a9.png)
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4 . 在正项等比数列
中,若
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a51841e33a9859ac254dc9f1284f279.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58857ee4f96f8ac657d7fec10f6cc58a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a51841e33a9859ac254dc9f1284f279.png)
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5 . 由正数组成的等比数列
中,若
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fd5e95f2b43bebc34535683520d7019.png)
__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ca39336552c21abdc99a41cf122c3b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fd5e95f2b43bebc34535683520d7019.png)
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甘肃省白银市会宁县会宁县第四中学2022-2023学年高二上学期期中数学试题(已下线)专题10 等比数列小题专项训练重庆市为明学校2022-2023学年高二上学期期末数学试题(已下线)4.3 等比数列(1)四川省成都市锦江区嘉祥外国语高级中学2022-2023学年高三上学期一诊模拟考试文科数学试题
6 . 已知在等比数列
中,
,在等差数列
中,
,则数列
的前9项和为___ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b28ef6f1b2279af482557a8ea46f2e43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0994074b7b7a383b5f4c39be60215f71.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4a4465705237c08e4e05d849cb28d0a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3307568267e448d3441db67e608d1d64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4a4465705237c08e4e05d849cb28d0a.png)
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7 . 正项递增等比数列
,若
,
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/708011adcd36510532a83a08920d8c8c.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4db7b6886fc235329e8bc0a82845e13.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b5eb911595c3a28522689b4d5d26269.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/708011adcd36510532a83a08920d8c8c.png)
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名校
解题方法
8 . 下列几种说法:
①在
ABC中,若
,则
;
②等差数列
中,若
,
,
成等比数列,则公比为
或1;
③在
ABC中,已知
,则
;
④数列
的前n项和
,则数列
是等差数列.
正确的序号有___________ .
①在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce4cba95fc7d4853a243f8e3fb20ce70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19dc38d888741a1b2e95fe0773a48c38.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca51be437b1a97ca92aa1159ab71102c.png)
②等差数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c1ccc6c74b8754e9bcbb3f39a11b6f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daf464629fa321a6ff7401ab79f07083.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
③在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce4cba95fc7d4853a243f8e3fb20ce70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a641da1c70d0ad481082af87e98ccbf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5b8b98b2f83279a49e94d9f48c5e6f2.png)
④数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a5df4d666ed956941509cae1ed53f26.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
正确的序号有
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9 . 已知
是
的等差中项,
是
,
的等比中项,则
等于___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8276d70443c3f3c3cbdf128fae8925c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/274a9dc37509f01c2606fb3086a46f4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8bf3d3564c61e5e9c39a9e2cf2de048b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18f0281e6bbdbe08beeccb55adf84536.png)
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10 . 在2,x,8,y四个数中,前三个数成等比数列,后三个成等差数列,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5113986d9507fc5015e71989831c128b.png)
___________
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5113986d9507fc5015e71989831c128b.png)
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