设数列{an}的前n项和为Sn,a1=10,a(n+1)=9Sn+10

问题描述:

设数列{an}的前n项和为Sn,a1=10,a(n+1)=9Sn+10

S(n+1)=Sn+a(n+1)=10Sn+10
S(n+1)+10/9=10*(Sn+10/9)
Sn+10/9 成等比数列,q=10
S1+10/9=10+10/9=100/9
Sn+10/9=10*(n-1)*(S1+10/9)=10*(n-1)*100/9
Sn=(n-1)*1000/9-10/9=(1000n-1010)/9