设数列{a n }的前n项和为S n ,对任意的正整数n,都有a n =5S n +1成立,记 .
来源:学生作业帮 编辑:作业帮 分类:数学作业 时间:2024/07/18 05:26:59
设数列{a n }的前n项和为S n ,对任意的正整数n,都有a n =5S n +1成立,记![]() (I)求数列{b n }的通项公式; (II)记 ![]() |
(I)∵a n =5S n +1,∴当n=1时,a 1 =5a 1 +1,∴
,
当n≥2时,a n =5S n +1,a n﹣1 =5S n﹣1 +1,两式相减,a n ﹣a n﹣1 =5a n ,即
,
∴数列{a n }成等比数列,其首项
a n ﹣1,
∴数列{a n }成等比数列,其首项a 1 =﹣
,公比是q=﹣
,
∴
,∴
.
(Ⅱ)由(Ⅰ)知
,
,
∴
,
∴
=
.
![](http://img.wesiedu.com/upload/7/ca/7ca85836af211b3274fe837660040eaa.jpg)
当n≥2时,a n =5S n +1,a n﹣1 =5S n﹣1 +1,两式相减,a n ﹣a n﹣1 =5a n ,即
![](http://img.wesiedu.com/upload/e/fe/efe8538b78f5a9cdfd32addaf5491607.jpg)
∴数列{a n }成等比数列,其首项
![](http://img.wesiedu.com/upload/c/f9/cf94e687d7b00f9f1e16bb3790a50b2a.jpg)
∴数列{a n }成等比数列,其首项a 1 =﹣
![](http://img.wesiedu.com/upload/3/3e/33e2c81c2e841c2971eefac98bb57d0c.jpg)
![](http://img.wesiedu.com/upload/a/f6/af68e08ba0b869d0631494b2d9e6ba98.jpg)
∴
![](http://img.wesiedu.com/upload/e/fe/efe55f18616a866e3dcab853b313a313.jpg)
![](http://img.wesiedu.com/upload/9/88/98898f14e12cf3ce8f9cf59288bea0b6.jpg)
(Ⅱ)由(Ⅰ)知
![](http://img.wesiedu.com/upload/7/01/7015bee434e276910346b5724a1aff30.jpg)
![](http://img.wesiedu.com/upload/0/8e/08e1f77ab849afc6a97c2b46b9e90841.jpg)
∴
![](http://img.wesiedu.com/upload/0/f6/0f6bfb41f24498364d8a9ca7493065c5.jpg)
∴
![](http://img.wesiedu.com/upload/d/86/d864933eb218fced063b07343c745f49.jpg)
![](http://img.wesiedu.com/upload/e/e6/ee611fd6998d9bcc3ab8218156de5d2e.jpg)
设数列an的前n项和为sn,对任意的正整数n,都有an=5sn+1成立,记bn=(4+an)/(1-an)(n是正整数)
已知等差数列an的首项a1为a,设数列的前n项和为Sn,且对任意正整数n都有a2n/an=4n-1/2n-1,求数列的通
数列{a(n)}的前n项和为S(n),a(1)=1,a(n+1)=2S(n)(∈正整数N).求数列{a(n)}的通项公式
已知S小n是数列{a小n}的前n项和,并且a1=1,对任意正整数n,S小n加1=4a小n加2,设b小n=a小n加1 减
数列{an}的前n项和为Sn,对任意的正整数n,都有an=5Sn+1成立,记bn=(4+an)/(1-an)(n是正整数
数列an的前n项和为sn,存在常数A,B,C使得an+sn=An^2+Bn+C对任意正整数n都成立.
一道高一期末考试题设数列{ An }的前n项和为Sn,对任意的正整数 n ,都有 An=5Sn+1 成立,记Bn=(4+
设数列{an}的前n 项和为Sn,对于任意的正整数n,都有an=5Sn+1成立,设bn=(4+an)/(1-an)(n∈
设数列{an}的前n项和为Sn,且对任意正整数n,an+Sn=4096.
数列,超难设数列{an}的前n项和为Sn,对任意的正整数n,都有an=5Sn+1成立,记bn=(4+an)/(1-an)
已知数列{an}的前n项和为Sn,且a1=2,3Sn=5an-A(n-1)+3S(n-1)(n≥2,n属于N*)设bn=
设数列(an )的前n 项和为S ,且对任意正整数n ,an +Sn =4096 求数列的通项公式