{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______.-数学

题目简介

{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______.-数学

题目详情

{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______.
题型:填空题难度:中档来源:不详

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-class="stub"1
2
a1
a1
=class="stub"1
2

当d=0时,{bn}的公比q=
a3
a1
=1
∴{bn}的公比为class="stub"1
2
或1
故答案为:class="stub"1
2
或1

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