已知实数等比数列{an}前n项和为Sn,S3=14,S6=126. (1)求数列{an}的通项公式an; (2)求数列{lgan}前n项的和Tn.
问题描述:
已知实数等比数列{an}前n项和为Sn,S3=14,S6=126.
(1)求数列{an}的通项公式an;
(2)求数列{lgan}前n项的和Tn.
答
(1)∵S3=a1+a2+a3=14,S6=a1+a2+…+a6=126∴a4+a5+a6=112,∵数列{an}是等比数列,∴a4+a5+a6=(a1+a2+a3)q3=112∴q3=8∴q=2由a1+2a1+4a1=14得,a1=2,∴an=a1qn-1=2n(2)∵an=2•2n-1=2n∴lgan=nlg2∴数列{lgan...