已知数列
满足
,且
是等比数列.
(1)求
的通项公式;
(2)求数列
的前n项和
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/552541f23dee78fa5303d9058e7ab8a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d82c65a855b1eed9c43e6829f6c3bffb.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82abda55b8bf0510c64ec3a2e2ca56ad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
更新时间:2023-03-01 14:33:23
|
相似题推荐
【推荐1】在①
;②
;③
,三个条件中任选一个,补充到下面问题的横线处,并解答.
已知数列
的前
项和为
,且
,______.
(1)
;
(2)设
求数列
的前
项和
.
注:如果选择多个条件解答,按第一个解答计分.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/004a0a7dff928ba46fda00938f8ebbce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7f90644b6975990131409ecc7c17be9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3c07d6d0c63061e09e36b5a2c74760b.png)
已知数列
![](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/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
(2)设
![](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)
注:如果选择多个条件解答,按第一个解答计分.
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【推荐2】已知数列
,其中
,数列
的前
项和
,数列
满足
.
(1)求数列
的通项公式;
(2)是否存在自然数
,使得对于任意
,
,有
恒成立?若存在,求出
的最小值;
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c2a0c55f9d913218c2e9700af6d4c5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ea8d0e50065114b05ef2dc1ea1129cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4be2164a2c67d6163faee87a10942bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50f230e299387b274047461c8d467adc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43b7e7cd571c8cd141cbbfe5d0890bf6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef24ecc1030ca02d6df6ea92beb2707f.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c2a0c55f9d913218c2e9700af6d4c5f.png)
(2)是否存在自然数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc93deaeab6d6c0b3bba5b88f5f025ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ece1cabeedc0da3de06bd8b7753cdf52.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe02fd7e84835e21d094a195170a27a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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【推荐1】等比数列
的各项均为正数,
,
,
成等差数列,且满足
.
Ⅰ
求数列
的通项公式;
Ⅱ
设
,
,求数列
的前n项和
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe229b24e2d56ff6b491725ceae4ff2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aafd638cfab8458087f7a97e2b6fce6c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d199f9235e3bd36bfa78c3772e941896.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c586c1b066cf6dacc4098d200b34d18.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/526acdde3f26ac3fd44a9c0bbbee706c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11d71379442f28c038d367d49422cf90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/987517758fad59f6f695761deb2a5ebd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe229b24e2d56ff6b491725ceae4ff2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11d71379442f28c038d367d49422cf90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/987517758fad59f6f695761deb2a5ebd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30e3a2311aa3f04ad843732960970424.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cea4ac187cbb465180e89f38250b3970.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bee4464b3b4eb6e52ee02f095aae84f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b708c8dcb2d66eb2ce0b3718a9cd924a.png)
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【推荐2】设正项等比数列
,
,且
的等差中项为
.若数列
满足![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72009607cefc110633e624b222c8781a.png)
.
(1)求数列![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d941370dd732aaf20d56797bc1fae0dd.png)
的通项公式;
(2)数列
前n项和为
,若不等式
对一切
恒成立,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50e4671fb7d933ef29ed2ab78d6d54dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe61d313eeca8ba47478a9de40540db8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bcd7dab04da0a263753bd13c8a6c5e17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72009607cefc110633e624b222c8781a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75f3ef9068c15d522018a6e2f01b3778.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d941370dd732aaf20d56797bc1fae0dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(2)数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6452492783a2d3618424f8cf73bd7781.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f841a990c38b0a56ab9b7cf4b5cc5e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cea4ac187cbb465180e89f38250b3970.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
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【推荐1】已知
为公差不为零的等差数列,其中
成等比数列,
.
(1)求数列
通项公式;
(2)记
,设
的前
项和为
,求最小的正整数
,使得
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a18556fda4a825861f1170cdeb059ff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28d84ee688592caf22e84910db79e7d0.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50a813139b92a24e1124ef96e3e485f5.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/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f366101c6ddf083aea62e38a1a2b483.png)
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解题方法
【推荐2】已知数列{an}为等差数列,S2=0,S6﹣S3=21.
(1)求数列{an}的通项公式;
(2)设bn
,求数列{bn}的前n项和Tn.
(1)求数列{an}的通项公式;
(2)设bn
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50440b23115963817529e267f194166c.png)
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