已知等差数列{an}是单调数列,且a1,a3,a4成等比数列,Sn为数列{an}的前n项和,则(S3-S2)/ (S5-S3)的值为?
人气:231 ℃ 时间:2019-08-18 17:07:09
解答
设公差为d,因为a1,a3,a4成等比数列,(a1+2d)/a1=(a1+3d)/(a1+2d)
2d/a1+1=1+d/(a1+2d)
2a1+4d=a1
a1=-4d
则(S3-S2)/ (S5-S3)
=a3/(a5+a4)
=(a1+2d)/(a1+4d+a1+3d)
=(2d-4d)/(4d-4d-4d+3d)
=-2d/-d
=2
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