> 数学 >
在等差数列{an}中,公差d≠0,且a1,a3,a7成等比例数列,则
a1+a3
a2+a4
=______.
人气:256 ℃ 时间:2019-11-23 10:16:51
解答
由题意可得a32a1a7
(a1+2d)2a1(a1+6d)
解之可得d=
a1
2
,或d=0(舍去)
a1+a3
a2+a4
=
a1+(a1+2×
a1
2
)
a1+
a1
2
+(a1+3×
a1
2
)
=
3a1
4a1
=
3
4

故答案为:
3
4
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