数列{a的n次幂}的前n项和为S的n次幂,a1=10,a的n+1次幂=9S的n次幂+10.求{lga的n次幂}为等差数列 超级急 考试中
人气：301 ℃ 时间：2020-01-09 06:53:11
解答
a(n+1)=9Sn+10
9Sn=a(n+1)-10
9S(n-1)=an-10
所以9an=a(n+1)-an
a(n+1)=10an
所以{an}是公比为10的等比数列
an=a1*10^(n-1)=10^n
lgan=lg10^n=n
所以{lgan}是公差为1的等差数列
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