已知等比数列{an},首项为81,数列{bn}满足bn=㏒3an,其前n项和为Sn,求证﹛bn﹜为等差数列.

缺少条件,{an}为正项数列,否则log3(an)无意义,题目没法解.

证：
数列为正项数列,公比q>0
a(n+1)/an=q
b(n+1)-bn=log3[a(n+1)]-log3(an)=log3[a(n+1)/an]=log3(q),为定值.
数列{bn}是等差数列.