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
问题描述：
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
答
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
答
{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...