若a1、a2、a3成等比数列,则a22=a1•a3
(a1+d)2=a1(a1+2d)
a12+2a1d+d2=a12+2a1d
d2=0
d=0 与条件d≠0矛盾
若a1、a2、a4成等比数列,则a22=a1•a4
(a1+d)2=a1(a1+3d)
a12+2a1d+d2=a12+3a1d
d2=a1d
∵d≠0
∴d=a1
则
a1 |
d |
若a1、a3、a4成等比数列,则a32=a1•a4
(a1+2d)2=a1(a1+3d)
a12+4a1d+4d2=a12+3a1d
4d2=-a1d
∵d≠0
∴4d=-a1
则
a1 |
d |
若a2、a3、a4成等比数列,则a32=a2•a4
(a1+2d)2=(a1+d)(a1+3d)
a12+4a1d+4d2=a12+4a1d+3d2
d2=0
d=0 与条件d≠0矛盾
综上所述:
a1 |
d |
a1 |
d |
故答案为1或-4