问题 填空题

{an}是等差数列,若a1,a3,a4是等比数列{bn}的连续三项,则{bn}的公比为______.

答案

∵{an}是等差数列,设公差为d,则a3=a1+2d,a4=a1+3d

∵a1,a3,a4是等比数列{bn}的连续三项,

∴a32=a1×a4

即(a1+2d)2=a1(a1+3d),

解得a1=-4d,或d=0

当a1=-4d时,{bn}的公比q=

a3
a1
=
a1-
1
2
a1
a1
=
1
2

当d=0时,{bn}的公比q=

a3
a1
=1

∴{bn}的公比为

1
2
或1

故答案为:

1
2
或1

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