设等比数列{an}前n项和为Sn,若S8:S4=2:3,则S12:S4=?9

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设等比数列{an}前n项和为Sn,若S8:S4=2:3,则S12:S4=?9设等比数列{an}前n项和为Sn,若S8:S4=2:3,则S12:S4=?9设等比数列{an}前n项和为Sn,若S8:S4=

设等比数列{an}前n项和为Sn,若S8:S4=2:3,则S12:S4=?9
设等比数列{an}前n项和为Sn,若S8:S4=2:3,则S12:S4=?9

设等比数列{an}前n项和为Sn,若S8:S4=2:3,则S12:S4=?9
S4、S8-S4、S12-S8成等比数列
公比为：(S8-S4)/S4=S8/S4-1=-1/3 (S12-S8)/S4=S12/S4-2/3=(-1/3)^2=1/9 S12/S4=7/9

S8=a1*d^7 S4=a1*d^3
S8:S4=d^4:1=2:3
S12:S4=(a1*d^11):(a1*d^3)=d^8:1=(d^4)²:1=4:9

我认为这道题有问题：设等比为列公比为q，则(S8-S4):S4=q^4=-1/3，这不是笑话吗？

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