已知等差数列{an}满足a6/a4=7/11

来源：百度知道编辑：UC知道时间：2024/05/24 12:29:46

已知等差数列{an}满足a6/a4=7/11，且Sn是此数列的前n项的和，则S11/S7=？

S11/S7
=[(a1+a11)*11/2]/[(a1+a7)*7/2]
=(2*a6*11/2)*(2*a4*7/2)
==(11/7)*(a6/a4)
=1

a6/a4=7/11
(a5+d)/(a5-d)=7/11
7a5-7d=11a5+11d
4a5=-18d
a5=-9d/2

s11=(a1+a10)*10/2
=5(a5-4d+a5+5d)
=5(2a5+d)
=5*(-9d+d)
=-40d

s7=(a1+a7)*7/2
=7(a5-4d+a5+2d)/2
=7(2a5-2d)/2
=7(a5-d)
=7(-9d/2-d)
=-77d/2

S11/S7=-40d/(-77d/2)=80/77

(a1+5d)/(a1+3d)=7/11
a1=-17d/2
S11/S7=[(a1+a11)*11]/[(a1+a7)*7]=1(将a1=-17d/2代入即可)

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