问题 选择题
等差数列{an}的公差d≠0,且a1,a3,a4成等比数列,Sn是数列{an}的前n项和,则
S4-S2
S5-S3
的值为(  )
A.3B.
5
7
C.
7
5
D.1
答案

∵等差数列{an}的公差d≠0,且a1,a3,a4成等比数列,

(a1+2d)2=a1•(a1+3d)

解得a1=-4d,

S4-S2
S5-S3
=
(4a1+
4×3
2
d)-(2a1+
2×1
2
d)
(5a1+
5×4
2
d)-(3a1+
3×2
2
d)

=

(-16d+6d)-(-8d+d)
(-20d+10d)-(-12d+3d)

=3.

故选A.

单项选择题
单项选择题