等比数列中前n项和为Sn 若S6/S2=7则S8/S4为?

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等比数列中前n项和为Sn 若S6/S2=7则S8/S4为?
等比数列中前n项和为Sn 若S6/S2=7则S8/S4为?

等比数列中前n项和为Sn 若S6/S2=7则S8/S4为?
S6/S2=7
[a1(1-q^6)/(1-q)]/[a1(1-q^2)/(1-q)]=7
(1-q^6)/(1-q^2)=7
(1-q^2)(1+q^2+q^4)/(1-q^2)=7
1+q^2+q^4=7
q^4+q^2-6=0
(q^2+3)(q^2-2)=0
因为q^2+3>0
所以q^2-2=0
q^2=2
S8/S4
=[a1(1-q^8)/(1-q)]/[a1(1-q^4)/(1-q)]
=(1-q^8)/(1-q^4)
=(1-q^4)(1+q^4)/(1-q^4)
=1+q^4
=1+(q^2)^2
=1+2^2
=5

S6=a+aQ+aQ2+aQ3+aQ4+aQ5
S2=a+aQ
S6/S2=1+Q+(Q2+Q3)+(Q4+Q5)/(1+Q)=1+Q2+Q4=(1/2)2+Q2+Q4=7-3/4
Q2=2
S8/S4=1+Q4=5

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