已知点(n,an)在函数f(x)=-2x-2的图象上,数列{an}的前n项和为Sn,数列{bn}的前n项和为Tn且Tn是6Sn与8n的等差中项1)求数列{bn}的通项公式2)设cn=bn+8n+3,数列{dn}满足d1=c1,d(n+1)=cd,求数列{dn}的前n项和Dn设cn=bn+8n+3,数列{dn}满足d1=c1,d(n+1)=cdn,求数列{dn}的前n项和Dn
问题描述:
已知点(n,an)在函数f(x)=-2x-2的图象上,数列{an}的前n项和为Sn,数列{bn}的前n项和为Tn
且Tn是6Sn与8n的等差中项
1)求数列{bn}的通项公式
2)设cn=bn+8n+3,数列{dn}满足d1=c1,d(n+1)=cd,求数列{dn}的前n项和Dn
设cn=bn+8n+3,数列{dn}满足d1=c1,d(n+1)=cdn,求数列{dn}的前n项和Dn
答
(1)、点(n,an)在函数f(x)=-2x-2的图象上an=-2n-2Sn=n(a1+an)/2=n(-4-2n-2)/2=-n^2-3nTn是6Sn与8n的等差中项2Tn=6Sn+8n=-6n^2-10nTn=-3n^2-5nT(n-1)=-3(n-1)^2-5(n-1)=-3n^2+n+2bn=Tn-T(n-1)=-6n-2检验:n=1时 T1=b1=...