已知数列{an}是首项为a1的等比数列,则能保证4a1,a5,-2a3成等差数列的公比q的个数为( ) A.0 B.1 C.2 D.3
问题描述:
已知数列{an}是首项为a1的等比数列,则能保证4a1,a5,-2a3成等差数列的公比q的个数为( )
A. 0
B. 1
C. 2
D. 3
答
∵4a1,a5,-2a3成等差数列,
∴2a5=4a1+(-2a3).
设数列{an}的公比为q,则a5=a1q4,a3=a1q2,
∴2a1q4=4a1-2a1q2.∵a1≠0,∴q4+q2-2=0,
∴q2=1或q2=-2(舍去),∴q=1或q=-1.
故选:C