1 . 已知数列
满足
,
.
(1)求证:数列
是等比数列,并求数列
的通项公式;
(2)记数列
的前
项中最大值为
,最小值为
,令
,称数列
是数列
的“中程数数列”.
①求“中程数数列”
的前
项和
;
②若
(
且
),求所有满足条件的实数对
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c41c8c4a4d20ddc700057c7df03c791d.png)
(1)求证:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2bf3da897eb73b729f66bb0d700775c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)记数列
![](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/6ddad3d9fdb5e9951b6a1c31f9a72a71.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0a625b91e0eba33b107550ee2a1e2f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/293570f1284f5161d0c9e83c1aef7777.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
①求“中程数数列”
![](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)
②若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e195bfeee892169b583158ad2363f5f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/faf534a50982614f697e616657822285.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4c428c12bd1ab65b447a57547b33302.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efa6e6840235cbfe76f9827fc755d4cc.png)
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2021-01-22更新
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3卷引用:福建省龙岩第一中学2022-2023学年高二上学期第二次月考数学试题