已知{an}是等差数列,且公差d≠0,又a1,a2,a4依次成等比数列,则a1+a4+a10a2+a4+a1=______.-数学

题目简介

已知{an}是等差数列,且公差d≠0,又a1,a2,a4依次成等比数列,则a1+a4+a10a2+a4+a1=______.-数学

题目详情

已知{an}是等差数列,且公差d≠0,又a1,a2,a4依次成等比数列,则
a1+a4+a10
a2+a4+a1
=______.
题型:填空题难度:中档来源:不详

答案

由{an}是等差数列,所以,a2=a1+d,a4=a1+3d,
又a1,a2,a4依次成等比数列,所以,a22=a1a4
(a1+d)2=a1(a1+3d),所以,a1d=d2,因为d≠0,所以,a1=d.
a1+a4+a10
a2+a1+a4
=
3a1+12d
3a1+4d
=class="stub"15d
7d
=class="stub"15
7

故答案为class="stub"15
7

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