1 . 设数列
的前
项和为
,
.
(1)求证:数列
是等比数列;
(2)若
,是否存在
的某些取值,使数列
中某一项能表示为另外三项之和?若能求出
的全部取值集合,若不能说明理由.
(3)若
,是否存在
,
,使数列
中,某一项可以表示为另外三项之和?若存在指出
的一个取值,若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.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/1ea9240a1100b786652d47c07f3f382b.png)
(1)求证:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d21cfd1ad0f4254be1d88c6577b6bbb2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99a1d64cfdcbe9c17e524b3db3ec74d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/832e8780cfa881b8b9ed283c0acb5af6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34a89c09d40f1ca26c70beadd071658b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
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2 . 已知数列
的前
项和
满足
,(
为常数,且
,
).
(1)求数列
的通项公式;
(2)设
,若数列
为等比数列,求
的值.
![](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/f66b976c36dbbea4262a64a7f74865d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20849c00c47cbdc43f18d53341b6c4e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c400a615a16a1662de98dfb4e49d58d3.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84f69929551a9d2e63f558183a1f94da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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3 . 记
为正项等比数列
的前n项和,若![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e4868f53987c18f71529d5c4b5d9a21.png)
(1)求数列
的公比q的值.
(2)若
,设
为该数列的前
项的和,
为为数列
的前n项和,若
,试求实数t的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e4868f53987c18f71529d5c4b5d9a21.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/097899de76881cab57ae4f6409662061.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b9a0d7150fb24be3e28ef7f0e18be93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2d51f9147b8265c0276c1f2c2659197.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/362832fa3d3c13c1eafd565349d66dce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2065a4d977f34f6e2c7512ce937a318.png)
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4 . 应届毕业生小李收到了两家公司的录用通知,录用的岗位相同,两家公司均提供税后年薪,且要求签约10年,A公司第一年的年薪为10万元,以后每年上涨20%;B公司第一年的年薪为20万元,以后每年上涨5%.
(I)如果只考虑收入水平,不考虑其他因素,你建议小李选择哪家公司?说明理由.
(I)如果只考虑收入水平,不考虑其他因素,你建议小李选择哪家公司?说明理由.
(II)十年内A公司提供的该岗位年薪能否超过B公司,若能,请指出从第几年开始,若不能,说明理由.
(参考数据:),
,
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