设数列{an}是公差不为零的等差数列,它的前n项和为Sn,且S1、S2、S4成等比数列,则a3a1等于(  ) A.2 B.3 C.4 D.5

问题描述:

设数列{an}是公差不为零的等差数列,它的前n项和为Sn,且S1、S2、S4成等比数列,则

a3
a1
等于(  )
A. 2
B. 3
C. 4
D. 5

数列{an}是公差不为0的等差数列,设公差为d,
S1,S2,S4成等比数列,则 S22=S1•S4
∴( 2a1+d)2=a1•(4a1+6d),化简可得 d=2a1

a3
a1
=
a1+2d
a1
=5.
故选:D.