已知等比数列
是递增数列,其公比为q,前n项和为Sn,并且满足
,
是
和
的等差中项.
(1)求数列
的通项公式;
(2)若
,
,求使
成立的正整数n的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3692d1cd54aaa7e2321fff5142e5d2c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61d473bfcc52ebc119430335531488a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e88093a749c0d46e0ee931ecfaff925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daf464629fa321a6ff7401ab79f07083.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73ff47025ee95dc97d18b41893c6e82e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd597fd3e8cf7d5fb0de8c0f18bd785c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad2a4db77dc3983f99792e38f16068a3.png)
21-22高三上·山东济南·期中 查看更多[3]
山东省济南市莱芜第一中学2021-2022学年高三上学期期中数学试题山东省烟台市莱州市第一中学2021-2022学年高三上学期12月月考数学试题(已下线)热点07 数列与不等式-2022年高考数学【热点·重点·难点】专练(新高考专用)
更新时间:2021-12-04 15:46:35
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【推荐1】已知等差数列
的前n项和为
,公差
,
,
,
成等差数列,
,
,
成等比数列.
(1)求
;
(2)记数列
的前n项和为
,
,证明数列
为等比数列,并求
的通项公式.
![](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/812be9806122241c476ba1db516c4823.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e0bd63f55069a3bc870915010b39225.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f30f56664446f32dbbc2c5f12a99374.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28b119c7e2b0e74a776e47d030d09087.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e88093a749c0d46e0ee931ecfaff925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daf464629fa321a6ff7401ab79f07083.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7da2f386b78cdf6489efaa2f5820d3e.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
(2)记数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36742d677e73dc7929d519a605d89c62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd08fe5d829c2f2fee4adc5957de3cd1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
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【推荐2】设数列
是各项为正数的等比数列,
是
和
的等差中项.
(1)求数列
的公比;
(2)若
,令
求数列
的前
项和
.
![](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/3e88093a749c0d46e0ee931ecfaff925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f78b34babe9ac0b93bd9e5c641117522.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ea8d0e50065114b05ef2dc1ea1129cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd0f044dc82a12fd1c71872f2ac12d06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
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【推荐1】在等比数列{an}中:
(1)已知a3+a6=36,a4+a7=18,an=
,求n;
(2)已知a5=8,a7=2,an>0,求an.
(1)已知a3+a6=36,a4+a7=18,an=
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
(2)已知a5=8,a7=2,an>0,求an.
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【推荐2】已知数列
为等差数列,
,
.
(1)求数列
的通项公式;
(2)若等比数列
满足
,
,求
的前
项和
,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e8c45e4c4ab30665338dd87a2258f23.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/305beb301b14f28592dee6f32a965240.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)若等比数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4995fa0403e013d888c0935ebfe15024.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fc9dc979ba069caf498a8df8fd66ce6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
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【推荐1】已知等差数列
满足
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满足首项为1,前3项和为7.
(1)求
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(2)求
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59c564b6250666accb7c3cf7775baafb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec4bdc2a6d4fc387dc621f0b5a268c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
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【推荐2】给出以下三个条件:①
;②
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已知公差不为0的等差数列
的前
项和为
,_______.
(1)求数列
的通项公式;
(2)若
,令
,求数列
的前
项和
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fca2cc2768794136c1e4da47d2f0873e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2df98ce180b9d9e1a83f2c1332e2da9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fddec3debcd4950f6f46f810d3071ec.png)
已知公差不为0的等差数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42040210bb7e102743a0ca1ca04ca5bc.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/feaf2150434e8c025122b6d5053ed4f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25c2a5f8ec179b72b201c3c0a670612a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
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