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-
a11 2 a1 1 2
当d=0时,{bn}的公比q=
=1a3 a1
∴{bn}的公比为
或11 2
故答案为:
或11 2