已知数列{an}是首项a1=4,公比q≠1的等比数列,Sn是其前n项和,且4a1,a5,-2a3成等差数列. (1)求公比q的值; (2)求Tn=a2+a4+…+a2n的值.

问题描述:

已知数列{an}是首项a1=4,公比q≠1的等比数列,Sn是其前n项和,且4a1,a5,-2a3成等差数列.
(1)求公比q的值;
(2)求Tn=a2+a4+…+a2n的值.

解 (1)由已知2a5=4a1-2a3
∴2a1q4=4a1-2a1q2
∵a1≠0,整理得q4+q2-2=0,
 解得q=1或q=-1,
又q≠1,∴q=-1;
(2)a2、a4、…、a2n构成a2为首项,以q2为公比的等比数列.
∴Tn=na2=-4n.