数列{an}中,a1=2,a2=3,且{anan+1}是以3为公比的等比数列,若bn=2a2n-1+a2n(n为正整数)a3 a4 a5 a6 都等于多少

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数列{an}中,a1=2,a2=3,且{anan+1}是以3为公比的等比数列,若bn=2a2n-1+a2n(n为正整数)a3 a4 a5 a6 都等于多少
数列{an}中,a1=2,a2=3,且{anan+1}是以3为公比的等比数列,若bn=2a2n-1+a2n(n为正整数)
a3 a4 a5 a6 都等于多少

数列{an}中,a1=2,a2=3,且{anan+1}是以3为公比的等比数列,若bn=2a2n-1+a2n(n为正整数)a3 a4 a5 a6 都等于多少
{a(n)a(n+1)}是首项为a(1)a(2)=6,公比为3的等比数列.
a(n)a(n+1)=6*3^(n-1) =2*3^n.
a(2n-1)a(2n)=2*3^(2n-1),
a(2n)a(2n+1)=2*3^(2n).
a(2n+1)/a(2n-1) = [a(2n)a(2n+1)]/[a(2n-1)a(2n)] = [2*3^(2n)]/[2*3^(2n-1)] = 3,
a(2n+1)=3a(2n-1),
{a(2n-1)}是首项为a(1)=2,公比为3的等比数列.
a(2n-1) = 2*3^(n-1).
a(2n) = [a(2n)a(2n-1)]/a(2n-1) = 2*3^(2n-1)/[2*3^(n-1)] =3^(n).
a(3)=2*3^(2-1) = 6,
a(5)=2*3^(3-1)=18.
a(4)=3^(2)=9.
a(6)=3^(3)=27,

ana(n+1)=qa(n-1)an,q=a(n+1)/q(an-1)=3,a(n+1)=3a(n-1)
a(2n+1)=3a(2n-1)=3^2a(2n-3)=3^3a(2n-5)=...
a(2n+1)=3a[2(n-1)+1]=3^2a[2(n-2)+1]=3^3a[2(n-3)+1]=...=3^na[2(n-n)+1]=3^na1=2*3^n
a(2n)=3a[2(n-1)]=3^2a[2(n-2)]=....3^(n-1)a{2[(n-(n-1)]}=3^(n-1)a2=3^n
a1=2,a2=3,a3=3a1=6,a4=3a2=9,a5=3a3=18,a6=3a4=27