已知等比数列{an}的各项都是正数,前n项和为Sn,且a3=4,S4=s2+12,求: (1)首项a1及公比q的值; (2)若bn=nan,求数列{bn}的前n项和Tn.

问题描述:

已知等比数列{an}的各项都是正数,前n项和为Sn,且a3=4,S4=s2+12,求:
(1)首项a1及公比q的值;
(2)若bn=nan,求数列{bn}的前n项和Tn

(1)由S4-S2=12,得a3+a4=12,则a4=8故q=a4a3=84=2,a1=a3q2=1(5分)(2)由(1)知:数列{an}的首项为1,公比为2的等比数列,an=2n-1,bn=n•2n-1,∴Tn=b1+b2+b3+bn=1+2•2+3•22++n•2n−12Tn=2+2•22+...