在数列{an}和{bn}中,bn是an和an+1的等差中项,a1=2且对任意n∈N*都有3an+1-an=0,则{bn}的通项bn=__________.
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![在数列{an}和{bn}中,bn是an和an+1的等差中项,a1=2且对任意n∈N*都有3an+1-an=0,则{bn}的通项bn=__________.](/uploads/image/z/3953764-28-4.jpg?t=%E5%9C%A8%E6%95%B0%E5%88%97%7Ban%7D%E5%92%8C%7Bbn%7D%E4%B8%AD%2Cbn%E6%98%AFan%E5%92%8Can%2B1%E7%9A%84%E7%AD%89%E5%B7%AE%E4%B8%AD%E9%A1%B9%2Ca1%3D2%E4%B8%94%E5%AF%B9%E4%BB%BB%E6%84%8Fn%E2%88%88N%2A%E9%83%BD%E6%9C%893an%2B1-an%3D0%2C%E5%88%99%7Bbn%7D%E7%9A%84%E9%80%9A%E9%A1%B9bn%3D__________.)
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在数列{an}和{bn}中,bn是an和an+1的等差中项,a1=2且对任意n∈N*都有3an+1-an=0,则{bn}的通项bn=__________.
在数列{an}和{bn}中,bn是an和an+1的等差中项,a1=2且对任意n∈N*都有3an+1-an=0,则{bn}的通项bn=__________.
在数列{an}和{bn}中,bn是an和an+1的等差中项,a1=2且对任意n∈N*都有3an+1-an=0,则{bn}的通项bn=__________.
3a(n+1)-an=0
a(n+1)/an=1/3
∴an是等比数列
an=a1*(1/3)^(n-1)
=2*(1/3)^(n-1)
a(n+1)=2*(1/3)^n
,bn是an和a(n+1)的等差中项
2bn=2*(1/3)^(n-1)+2*(1/3)^n
bn=(1/3)^(n-1)+(1/3)^n
=3*(1/3)^n+(1/3)^n
=4*(1/3)^n