设数列{an}的前几项和为Sn,a1=10 an+1=9Sn+10 求证{lgan}是等差数列半小时内解决

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设数列{an}的前几项和为Sn,a1=10 an+1=9Sn+10 求证{lgan}是等差数列半小时内解决

设数列{an}的前几项和为Sn,a1=10 an+1=9Sn+10 求证{lgan}是等差数列半小时内解决
设数列{an}的前几项和为Sn,a1=10 an+1=9Sn+10 求证{lgan}是等差数列
半小时内解决

设数列{an}的前几项和为Sn,a1=10 an+1=9Sn+10 求证{lgan}是等差数列半小时内解决
你要的答案是:
An+1=9Sn+10
An=9S(n-1)+10
An=Sn-S(n-1)=(1/9)[A(n+1)-An]
A(n+1)/An=10
所以为等比数列 A1=10,q=10
An=10*10^(n-1)=10^n
Bn=lgAn=n
B(n+1)-Bn=n-(n-1)=1
1为常数,所以是等差数列

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