1 . 成等差数列的三个正数的和等于15,并且这三个数分别加上2、5、13后成为等比数列{bn}中的b3、b4、b5.
(Ⅰ)求数列{bn}的通项公式;
(Ⅱ)数列{bn}的前n项和为Sn,求证:数列{Sn+
}是等比数列.
(Ⅰ)求数列{bn}的通项公式;
(Ⅱ)数列{bn}的前n项和为Sn,求证:数列{Sn+
![](https://img.xkw.com/dksih/QBM/2017/1/6/1619444287930368/1619444288266240/STEM/fb869952a2da4844bbb954ac11b6da73.png)
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2016-12-03更新
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12卷引用:天津市河西区2023-2024学年高二上学期期末质量调查数学试卷
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真题
2 . 在数列
与
中,
,数列
的前
项和
满足
,
为
与
的等比中项,
.
(Ⅰ)求
的值;
(Ⅱ)求数列
与
的通项公式;
(Ⅲ)设
.证明
.
![](https://img.xkw.com/dksih/QBM/2010/4/1/1569688487706624/1569688630157312/STEM/813be1cf542c45798e71fdc7ba882344.png)
![](https://img.xkw.com/dksih/QBM/2010/4/1/1569688487706624/1569688630157312/STEM/0b1f298ceb954a558ea1f4fad3f29af0.png)
![](https://img.xkw.com/dksih/QBM/2010/4/1/1569688487706624/1569688630157312/STEM/548ebffc86384a838d27814ae64fc871.png)
![](https://img.xkw.com/dksih/QBM/2010/4/1/1569688487706624/1569688630157312/STEM/813be1cf542c45798e71fdc7ba882344.png)
![](https://img.xkw.com/dksih/QBM/2010/4/1/1569688487706624/1569688630157312/STEM/a38d1b920aec483c96206d43eee90ac4.png)
![](https://img.xkw.com/dksih/QBM/2010/4/1/1569688487706624/1569688630157312/STEM/7a676c7243304dfdb9036b8769b2a157.png)
![](https://img.xkw.com/dksih/QBM/2010/4/1/1569688487706624/1569688630157312/STEM/1d0f16dc5a4f41d3adf5f484b898c9f2.png)
![](https://img.xkw.com/dksih/QBM/2010/4/1/1569688487706624/1569688630157312/STEM/be312a87633e46cf81335e2fc434e3db.png)
![](https://img.xkw.com/dksih/QBM/2010/4/1/1569688487706624/1569688630157312/STEM/b864f3e861b5427aa2be157dbb8a4e60.png)
![](https://img.xkw.com/dksih/QBM/2010/4/1/1569688487706624/1569688630157312/STEM/4348208411b44f8189ae0182150f73a9.png)
![](https://img.xkw.com/dksih/QBM/2010/4/1/1569688487706624/1569688630157312/STEM/c70e00a82c7a45f09ba87c7ab1646276.png)
(Ⅰ)求
![](https://img.xkw.com/dksih/QBM/2010/4/1/1569688487706624/1569688630157312/STEM/e9b838c4e6534ea69e1262eb353cf9af.png)
(Ⅱ)求数列
![](https://img.xkw.com/dksih/QBM/2010/4/1/1569688487706624/1569688630157312/STEM/813be1cf542c45798e71fdc7ba882344.png)
![](https://img.xkw.com/dksih/QBM/2010/4/1/1569688487706624/1569688630157312/STEM/0b1f298ceb954a558ea1f4fad3f29af0.png)
(Ⅲ)设
![](https://img.xkw.com/dksih/QBM/2010/4/1/1569688487706624/1569688630157312/STEM/e32a4e148ded498aa8086a9b5eff70e9.png)
![](https://img.xkw.com/dksih/QBM/2010/4/1/1569688487706624/1569688630157312/STEM/fc145be6d0fe45cba96e4235a4dc4739.png)
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