23-24高二上·全国·课后作业
解题方法
1 . 已知等差数列
的前n项和为
.
(1)求证:
,
,
成等差数列;
(2)求证:
,
,
成等差数列;
(3)试推广(1)和(2)的结果,写出你的结论并加以证明.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e0bd63f55069a3bc870915010b39225.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e147c1f8b0941586a7cc61e9b0d7879.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a012e9ffdbe44925133a1754e9031fae.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6899bf9cadae2ccdb14cbc87d4f280ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/142bd84f63530e1fdf2cc53ab3a14037.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4740344514cb6f1de52d3a2d8c3ee087.png)
(3)试推广(1)和(2)的结果,写出你的结论并加以证明.
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23-24高二上·全国·课后作业
2 . 已知等差数列
的前n项和为
,且
,
,求
.
![](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/5170584604571b5e1afd5ece941e2e73.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3aa54a479e4178d698818f69d859fe13.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05201ef79a5d5904f492845396fb5470.png)
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21-22高二·江苏·课后作业
解题方法
3 . 对任意的等差数列
,计算
,
,
,
,…你发现了什么一般规律?能将发现的规律推广吗?在等比数列中有怎样类似的结论?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e6f19b84484b5480ea2100165abfd81.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ab5a181478e9c2307d9a934d891621d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c273b7656ae822a6d802c09396e49bcd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1fc5262813142d25b25f43dcb119e627.png)
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21-22高二·江苏·课后作业
4 . 设等差数列{an}的前n项和Sn,若S8=100, S16=392,求S24.
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21-22高二·江苏·课后作业
5 . 设等差数列
的前n项和为
.
(1)已知
,
,求
;
(2)已知
,
,求
;
(3)已知
,
,求
;
(4)已知
,
,求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
(1)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/618715534c33e403ba189272a5fbf478.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e3931e6266decbab4ab76b280f61bda.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7eed39c7d611309b01476c15ab242308.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92d3b466840923657b69ff10d3a5f337.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af2a5276a68aa36c24e2032df45d9568.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/711161d23bed5161de370857a687c3ea.png)
(3)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/febb4122ef4e047993a99582cc6ff35d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ebeddc8c10d098573832edcb72d91f74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a27c112387e56c976489fa484c0d48f.png)
(4)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36183db0759eec0e108274d229fcd00b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76fddf75fdd0d4fd3dbefc7658b4a1e0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05201ef79a5d5904f492845396fb5470.png)
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20-21高二·全国·课后作业
6 . 已知等差数列
的前n项和为
,且
,求
的值.
![](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/8aa54f7899ecf02462458f432161469a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fa209ac86cd8c88e638cda47db5bfa2.png)
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