已知等差数列{an}的前n项和为Sn,且a2=1,S11=33.(1)求{an}的通项公式(2)设bn=(1/4)^an,求证:{bn}是等比数列,并求其前n项和Tn
来源:学生作业帮助网 编辑:作业帮 时间:2024/06/27 22:05:56
![已知等差数列{an}的前n项和为Sn,且a2=1,S11=33.(1)求{an}的通项公式(2)设bn=(1/4)^an,求证:{bn}是等比数列,并求其前n项和Tn](/uploads/image/z/5490215-71-5.jpg?t=%E5%B7%B2%E7%9F%A5%E7%AD%89%E5%B7%AE%E6%95%B0%E5%88%97%7Ban%7D%E7%9A%84%E5%89%8Dn%E9%A1%B9%E5%92%8C%E4%B8%BASn%2C%E4%B8%94a2%3D1%2CS11%3D33.%281%29%E6%B1%82%7Ban%7D%E7%9A%84%E9%80%9A%E9%A1%B9%E5%85%AC%E5%BC%8F%EF%BC%882%EF%BC%89%E8%AE%BEbn%3D%281%2F4%29%5Ean%2C%E6%B1%82%E8%AF%81%EF%BC%9A%7Bbn%7D%E6%98%AF%E7%AD%89%E6%AF%94%E6%95%B0%E5%88%97%2C%E5%B9%B6%E6%B1%82%E5%85%B6%E5%89%8Dn%E9%A1%B9%E5%92%8CTn)
已知等差数列{an}的前n项和为Sn,且a2=1,S11=33.(1)求{an}的通项公式(2)设bn=(1/4)^an,求证:{bn}是等比数列,并求其前n项和Tn
已知等差数列{an}的前n项和为Sn,且a2=1,S11=33.
(1)求{an}的通项公式
(2)设bn=(1/4)^an,求证:{bn}是等比数列,并求其前n项和Tn
已知等差数列{an}的前n项和为Sn,且a2=1,S11=33.(1)求{an}的通项公式(2)设bn=(1/4)^an,求证:{bn}是等比数列,并求其前n项和Tn
(1)
等差数列{an}
S11=11a1+55d=33
a2=a1+d=1
d=1/2
a1=1/2
an=(1/2)+(1/2)(n-1)
=(1/2)n
(2)
bn=(1/4)^an
bn+1=(1/4)^an+1
bn+1/bn=(1/4)^(an+1)/(1/4)^(an)=(1/4)^(an+1-an)=(1/4)^d
所以:{bn}是等比数列
b1=1/2
Tn=(1/2)(1-(1/2)^n)/(1-(1/2))=1-(1/2)^n
已知等差数列An的前n项和为Sn,且S13>0,S14
已知等差数列an的前n项和为Sn,且a1^2+a8^2
等差数列an的前n项和为Sn,已知Sm=a,Sn-Sn-m=b,m、n属于自然数且n>m,求Sn?
已知数列{an}的前n项和为Sn,且满足an+2Sn*Sn-1=0,a1=1/2.求证:{1/Sn}是等差数列
已知数列an是等差数列,且a1不等于0,Sn为这个数列的前n项和,求limnan/Sn.limSn+Sn-1/Sn+Sn-1
已知正数列{an}的前n项和为sn,且an,sn,1/an成等差数列,求an的通项公式,并用数学归纳法证明.
已知各项均为正数的数列{an}前n项和为Sn,首相为a1,且½,an,Sn是等差数列,求通项{an}公式
已知数列{an}中,其前n项和为Sn,且n,an,Sn成等差数列(N属于正整数).(1)求数列{an}已知数列{an}中,其前n项和为Sn,且n,an,Sn成等差数列(N属于正整数)。(1)求数列{an}的通项公式;(2)求Sn
已知等差数列an的前n项和为sn 且满足Sn=n²+n,则通项公式an=?
已知各项均为正数的数列{an}的前n项和为sn,且sn,an,1成等差数列,求数列{an}的通项公式
已知等差数列an的前n项和为Sn,且a4为10,S4为22,求通项公式,
已知等差数列an的前n项和为sn,且a6=1,则s11的值为
(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
已知等差数列{an}的前n项和为Sn,且S10=17,S20=17,则S30为?
已知数列an的前n项和为Sn,首项伟a1,且1,an,Sn成等差数列,求数列an的通项公式
高一数学已知数列an的前n项和为sn,且an,1,2sn成等差数列.求an通项
已知{an}{bn}都为等差数列,前n项的和分别为Sn,Tn,且Sn/Tn=5n/6n+1,求a5/b5.
求证等差数列!已知数列an的各项均为正数,前n项和为Sn,且满足2Sn=a∧2n+n-4