设数列{an}的前n项和为Sn,a1=10,a(n+1)=9Sn+10

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设数列{an}的前n项和为Sn,a1=10,a(n+1)=9Sn+10

设数列{an}的前n项和为Sn,a1=10,a(n+1)=9Sn+10
设数列{an}的前n项和为Sn,a1=10,a(n+1)=9Sn+10

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

s(1)=a(1)=10
a(n+1)=s(n+1)-s(n)=9s(n)+10
s(n+1)=10s(n)+10
s(n+1)+10/9=10[s(n)+10/9]
{s(n)+10/9}为首项为s(1)+10/9=100/9,公比为10的等比数列
s(n)+10/9=10^(n+1)/9
a(n+1)=9s(n)+10=10^(n+1)
a(n)=10^n

(1):a(n+1)=9Sn+10
(2):an=9S(n-1)+10
(1)-(2)=a(n+1)-an=9an
所以:a(n+1)=10an
{an}为首项是10,公比为10的等比数列。所以an=10*10^(n-1)=10^n

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