已知等比数列{an},首项为81,数列{bn}满足bn=log3为底an,其前n项和Sn

问题描述:

已知等比数列{an},首项为81,数列{bn}满足bn=log3为底an,其前n项和Sn
1)证明{bn}为等差数列
2)若S11≠S12,且S11最大,求{bn}的公差d的范围

(1)等比数列{an},首项为81设an=a1*q^(n-1)=81*q^(n-1)数列{bn}满足bn=log3为底an∴bn=log3为底[81*q^(n-1)]=log3为底81+log3为底q^(n-1)=4+(n-1)log3为底q=log3为底q*n+4-log3为底q∵log3为底q为常数,∴bn为以4为首...