Question

等比数列{an}a1=81,bn=log3an,前n项和味Sn.证{bn}为等差数列

Answer 1

a(n)=81*q^(n-1),

b(n)=log_{3}[a(n)] = log_{3} [81*q^(n-1)] = log_{3}(81) + log_{3}[q^(n-1)]

=4 + (n-1)log_{3}(q)

{b(n)}为首项为4,公差为log_{3}(q)的等差数列.