在等比数列{an}(n∈N+)中,a1>1,公比q>0.设bn=log2an,且b1+b3+b5=6,b1b3b5=0. (1)求证:数列{bn}是等差数列; (2)求{bn}的前n项和Sn及{an}的通项an.

问题描述:

在等比数列{an}(n∈N+)中,a1>1,公比q>0.设bn=log2an,且b1+b3+b5=6,b1b3b5=0.
(1)求证:数列{bn}是等差数列;
(2)求{bn}的前n项和Sn及{an}的通项an

(1)证明:由题意得,bn=log2an,∴bn+1-bn=log2an+1-log2an=logan+1an2=log2q为常数,∴数列{bn}是以公差d=log2q等差数列.(2)由(1)和b1+b3+b5=6,得3b3=6,即b3=2,∴b3=log2a3=2,得b3=2,∵a1>1,∴b1=log...