已知等差数列{an}中,a2,a4,a9成等比数列,则a1+a3+a5a2+a4+a6=______.-数学

题目简介

已知等差数列{an}中,a2,a4,a9成等比数列,则a1+a3+a5a2+a4+a6=______.-数学

题目详情

已知等差数列{an}中,a2,a4,a9成等比数列,则
a1+a3+a5
a2+a4+a6
=______.
题型:填空题难度:偏易来源:不详

答案

设等差数列的公差为d,由a2,a4,a9成等比数列,可得 ( a1+3d)2=(a1+d)(a1+8d),解得 d=0,或 d=3a1.
当 d=0时,等差数列{an}是常数数列,
a1+a3+a5
a2+a4+a6
=1.
当d=3a1 时,
a1+a3+a5
a2+a4+a6
=
a1+(a1+2d)+(a1+4d)
a1+d+a1+3d+a1+5d
=
21a1
301
=class="stub"7
10

故答案为 1 或class="stub"7
10

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