已知{an}是等差数列,其前n项和为Sn,已知a3=11,S9=153.(1)求数列{an}的通项公式；（2）设an=log2bn,证明{bn}是等比数列,求其前n项和Tn.

来源：学生作业帮助网编辑：作业帮时间：2024/05/05 21:58:10

已知{an}是等差数列,其前n项和为Sn,已知a3=11,S9=153.(1)求数列{an}的通项公式；（2）设an=log2bn,证明{bn}是等比数列,求其前n项和Tn.
已知{an}是等差数列,其前n项和为Sn,已知a3=11,S9=153.(1)求数列{an}的通项公式；（2）设an=log2bn,证明{bn}是等比数列,求其前n项和Tn.

已知{an}是等差数列,其前n项和为Sn,已知a3=11,S9=153.(1)求数列{an}的通项公式；（2）设an=log2bn,证明{bn}是等比数列,求其前n项和Tn.
(1)s9=9a5=153,a5=17
d=(a5-a3)/2=3,an=a3+(n-3)d=3n+2
(2) bn=2^an=2^(3n+2),bn-1=2^(3n-1) (注：n-1为下标）
　　bn/bn-1=2^3=8
∴{bn}是首项为32,公比为8的等比数列,Tn=32(1-8^n)/(1-8)=32(8^n-1)/7

已知数列an其前n项和为Sn,且Sn=3n^2+5n,求证数列an是等差数列已知an是等差数列,前n项和为Sn,求证:S3n=3(S2n-Sn) (1)已知数列an的前n项和为sn满足sn=an²+bn,求证an是等差数列(2)已知等差数列an的前n项和为sn,求证数列sn/n也成等差数列已知an是等差数列,其前n项和为sn,已知a3=-13,s9=-45 求通项数列「AN」绝对值的前十项和已知数列{an}为等差数列,Sn是其前n项和,a3=4,S3=18求等差数列{an}的通项公式设Sn为等差数列{An}的前n项和,求证：{Sn/n}是等差数列已知数列{an}前n项和为sn=3n^2-n,求证其为等差数列已知等差数列{an},是递增数列,且an不等于0,n属于N,其前n项和为Sn,若S7*S8 已知等差数列{an},是递增数列,且an不等于0,n属于N,其前n项和为Sn,若S7*S8 已知等差数列{an}的首项为4,公差为4,其前n项和为Sn,则数列{1/Sn}的前n项和为已知数列{an}中,an>0其前n项和为Sn,且Sn=1/8(an+2)²,求证：数列{an}为等差数列在等差数列{an}中,已知3a8=5a13,且a1>0,Sn为其前n项和.则Sn中最大的是( ) 已知数列an是等差数列,其前n项和为Sn,a3=6,求1/S1+1/S2+...+1/Sn 已知等差数列{an}中,a1＞0,3a8=5a13,其前n项和为Sn,则数列{Sn}中最大项是? 已知{an}是等差数列,其前n项和为Sn,已知a3=11,S9=153,求数列{an}的通项公式已知an是等差数列,其前n项和为sn,已知,a3等于11,s9等于153,求数列an的通项公式已知{an}是等差数列,其前n项和为Sn,已知a3=11,S9=153,求{an}的通项公式已知数列{an}的前n项和为Sn=n^2-3n,求证：数列{an}是等差数列