设数列{an}的前几项和为Sn,满足2Sn=an+1-2^n+1+1,且a1,a2+5.a3成等差数列(1)求a1的值(2)求数列{an}的通项公式

来源:学生作业帮助网 编辑:作业帮 时间:2024/04/29 06:32:40

设数列{an}的前几项和为Sn,满足2Sn=an+1-2^n+1+1,且a1,a2+5.a3成等差数列(1)求a1的值(2)求数列{an}的通项公式
设数列{an}的前几项和为Sn,满足2Sn=an+1-2^n+1+1,且a1,a2+5.a3成等差数列
(1)求a1的值
(2)求数列{an}的通项公式

设数列{an}的前几项和为Sn,满足2Sn=an+1-2^n+1+1,且a1,a2+5.a3成等差数列(1)求a1的值(2)求数列{an}的通项公式
2Sn=a(n+1)-2^(n+1)+1令n=1,2联立(a2+5)*2=a1+a3得a1=1
2an=2sn-2sn-1=a(n+1)-an-2^n
即a(n+1)=3an+2^n
所以a(n+1)+2^(n+1)=3*(an+2^n)
an+2^n=(a1+2^1)*3^(n-1)=3^n
an=3^n-2^n

2Sn=a(n+1)-2^(n+1)+1令n=1,2联立(a2+5)*2=a1+a3得a1=1
2an=2sn-2sn-1=a(n+1)-an-2^n
即a(n+1)=3an+2^n
所以a(n+1)+2^(n+1)=3*(an+2^n)
an+2^n=(a1+2^1)*3^(n-1)=3^n
an=3^n-2^n

已知数列An满足An>0,其前n项和为Sn为满足2Sn=An的平方+An(1)求An(2)设数列Bn满足An/2的n次方,Tn=b1+b2+ 设数列an的前n项和为Sn,满足an+sn=An^2+Bn+1(A不等于0)an为等差数列,求(B-1)/A 已知数列{an}的前n项和为Sn,满足an+Sn=2n. (Ⅰ)证明:数列{an-2}为等比数列,并求出an;已知数列{an}的前n项和为Sn,满足an+Sn=2n.(Ⅰ)证明:数列{an-2}为等比数列,并求出an;(Ⅱ)设bn=(2-n) 求:设数列 {an}的前n项和为Sn,数列{Sn}的前n项和为Tn,满足Tn=2Sn一n²,n∈求:设数列 {an}的前n项和为Sn,数列{Sn}的前n项和为Tn,满足Tn=2Sn一n²,n∈N 设数列{an}的前n项和为Sn,且满足Sn-Sn-1+2SnSn-1=0(n≥2)设数列{an}的前n项和为Sn,且满足Sn-S(n-1)+2SnS(n-1)=0(n≥2),a1=1/2.1 求证,数列{1/Sn}是等差数列 2 求an的通项公式 设数列{an}前n项和为Sn,且满足S1=2,S(n+1)=3Sn+2.一,证明数列是等比数列并...设数列{an}前n项和为Sn,且满足S1=2,S(n+1)=3Sn+2.一,证明数列是等比数列并求出通项?二,求数列{nan}的前n项的和Tn 设数列{an}的前几项和为Sn,满足2Sn=an+1-2^n+1+1,且a1,a2+5.a3成等差数列(1)求a1的值(2)求数列{an}的通项公式 设数列{an}的前n项和为Sn,且3Sn=an+4.(1)求数列{an}的通项公式;(2)若数列{bn}满足bn=3Sn,求数列...设数列{an}的前n项和为Sn,且3Sn=an+4.(1)求数列{an}的通项公式;(2)若数列{bn}满足bn=3Sn,求数 已知数列{an}中的前几项和为Sn且满足a1=0.5,an=-2Sn*S(n-1).证明数列{1/Sn}为等差数列,求Sn与an 设数列An的前n项和为Sn,满足2Sn=An+1 -2^n+1+1,且A1.A2+5.A3成等差数列 求数列的设数列An的前n项和为Sn,满足2Sn=An+1 -2^n+1+1,且A1.A2+5.A3成等差数列 求数列的通项公式 设数列{an}的前n项和为Sn,且满足S1=2,S(n+1)=3Sn+2(n=1,2,3) 设bn=2,S(n+1)=3Sn+2(n=1,2,3.) 注:n+1设数列{an}的前n项和为Sn,且满足S1=2,Sn+1=3Sn+2(n=1,2,3) 设bn=2,Sn+1=3Sn+2(n=1,2,3.)设bn=an比Sn平方,求证b1+b2+b3.bn 已知数列{an}的前n项和为sn,满足an+sn=2n ① 证明∶数列{an-2}为等比数列,并求出an ②设bn=(2-N)(an-2),求{bn}的最大项 数列(an),a1=1,当n≥2,其前n项和Sn满足Sn^2=an(Sn-1)证(1/Sn)是等差数列.设bn=log以2为底Sn/S(n+2),bn的前n项和Tn,求满足Tn≥6的最小正整数n 设数列{an}的前n项和为Sn,数列{Sn}的前n项和为Tn,满足Tn=2Sn-n^2,n∈N*.求a1的值以及an的通项公式. 设数列{an}的前n项和为Sn,数列{Sn}的前n项和为Tn,满足Tn=2Sn-n2,n∈N*.求a1的值以及an的通项公式. 若等差数列{an}的前n项和为Sn,且满足Sn/S2n为常数,则称该数列为S数列 若首项为a1的各项为正数的等差数列{an}是S数列,设n+h=2008,(n,h为正数) 求1/Sn+1/Sh的最小值 Sn、Sh分别是数列的前n项和和 已知数列{an},{bn}满足a1=2,2an=1+ana(n+1),bn=an-1,设数列{bn}的前n项和为Sn,Tn=S2n-Sn.求数列{bn}的通项公式. 设数列{an}的前n项和为Sn,对任意n∈N*满足2Sn=an(an+1),且an≠0 (1)求数列an的通项公式设数列{an}的前n项和为Sn,对任意n∈N*满足2Sn=an(an+1),且an≠0(1)求数列an的通项公式