已知数列
的前
项和为
,
,
.
(1)证明数列
为等差数列,并由此求出通项公式
;
(2)若数列
满足
,记
,求满足
成立最小自然数n的值.
注:已知等差数列
的公差
,
,则
![](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/b13a6e1d671215fc96e4bee3541d1096.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9eac6e07b578aa8ce60c44511e21bf78.png)
(1)证明数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/547a5fd14e74e24c0030a862283deb33.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
(2)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78a7f082a6eb1b89072e0858914d7aa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d41547fa86739cd0e68f5057410fe14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d2b8552749a9d1b48a1ae082b04e1a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a67b4fd219dd67ba8087d9b54f3fd2e.png)
注:已知等差数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/812be9806122241c476ba1db516c4823.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffa01f03fb074bff35b35e07047d11b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5644612f2bd1752f709363aaff430ac.png)
20-21高一下·江西·阶段练习 查看更多[2]
更新时间:2021-04-03 09:50:03
|
相似题推荐
【推荐1】从下面的表格中选出3个数字(其中任意两个数字不同行且不同列)作为递增等差数列
的前三项.
(1)求数列
的通项公式,并求
的前
项和
;
(2)若
,记
的前
项和
,求证
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
第1列 | 第2列 | 第3列 | |
第1行 | 7 | 2 | 3 |
第2行 | 1 | 5 | 4 |
第3行 | 6 | 9 | 8 |
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](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)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b4e5bb55dc85150de816e2d475e94aa.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)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9928e46511e601913619a427ded84a3.png)
您最近一年使用:0次
【推荐2】已知
是公差不为0的等差数列,
,且
成等比数列,数列![](https://staticzujuan.xkw.com/quesimg/Upload/formula/454ffe59d3fe8c2932dc239118941678.png)
,数列
的前
项和
.
(1)求![](https://staticzujuan.xkw.com/quesimg/Upload/formula/686ece75006ad358f23314dc8a246e11.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/039e4fe671d61e59b96ee525c9df43e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29b1b845916a4b6a18cdfbcd308d09c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/454ffe59d3fe8c2932dc239118941678.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b22a3371dc976b6b3d9cc29a70445b5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f329b217e1051b23f0d61023cdc6e69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/686ece75006ad358f23314dc8a246e11.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
您最近一年使用:0次
解答题-证明题
|
适中
(0.65)
名校
解题方法
【推荐1】已知数列
满足
,
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b967232e28ad0d453adc66676bdf8b2b.png)
(1)求证:数列
是等差数列;
(2)求数列
的前
项和
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b71f853a5f52f0c085431c60a4d4af2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d91dcf5da1c722a8a328ea8d0d789238.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b967232e28ad0d453adc66676bdf8b2b.png)
(1)求证:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41cf1da18d91f7c98086553d157d1a87.png)
(2)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7706e0dba93c9f25c28bc8b01de44b70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
您最近一年使用:0次
解答题-问答题
|
适中
(0.65)
解题方法
【推荐2】已知
是数列
的前n项和,
,
,
的等差中项为
.
(1)求
的通项公式;
(2)若
,求数列
的前n项和
.
![](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/b13a6e1d671215fc96e4bee3541d1096.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ebadf2b3ec3dc92cd902eff76085ad46.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d5680dc0a2c3470289c4bfc8d19ee24.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b537f22ff004aa2ae3a3080e0fb9a7ae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
您最近一年使用:0次
【推荐1】2020年是我国扶贫收官之年,为了防止已脱贫贫困户再次返贫,某村拟加大资金投入,帮助贫困户合作社扩大牧场规模并增加牛的存栏数.已知2020年初牧场牛的存栏数为240,预计以后每年存栏数的增长率为
,且在每年年底卖出20头牛,设牧场从2020年起每年年初的计划存栏数依次为
,…
(1)写出一个递推公式,表示
与
之间的关系;
(2)求
的值(精确到1).
(参考数据:
)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f62f732f992bfad07df911e39eac0bc4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/312893147a40a4cd5d46fc2ad309c488.png)
(1)写出一个递推公式,表示
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dedce3064cdaf30d62ee38aabc86030e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c59e7c7a84a4bdb959e95536d0404ceb.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cac8bfd10cba06ff5203cfef5b8b3292.png)
(参考数据:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ddb3743a961d655b2f821b44b0803a46.png)
您最近一年使用:0次
【推荐2】已知数列{an}的前n项和为
,
,
,求{an}的通项.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ea8d0e50065114b05ef2dc1ea1129cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7e375b8b3791ee98dab11cd97b6379f.png)
您最近一年使用:0次