设等比数列｛AN}的前N项和为SN.A1=1,S6=4S3,则A4=?

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设等比数列｛AN}的前N项和为SN.A1=1,S6=4S3,则A4=?
设等比数列｛AN}的前N项和为SN.A1=1,S6=4S3,则A4=?

设等比数列｛AN}的前N项和为SN.A1=1,S6=4S3,则A4=?
s6=4s3
q≠1
s6=a1(1-q^6)/(1-q)
=(1-q^6)/(1-q)
s3=a1(1-q^3)/(1-q)
=(1-q^3)/(1-q)
s6=4s3
(1-q^6)/(1-q)=4(1-q^3)/(1-q)
(1-q^6)=4(1-q^3)
(1-q^6)-4(1-q^3)=0
(1-q^3)[(1+q^3)-4]=0
(1-q^3)[(1+q^3)-4]=0
(1-q^3)(q^3-3)=0
q^3=3或q^3=1(舍去）
a4=a1q^3=1*3=3

S6=4S3
a1(1-q^6)/(1-q)=4a1(1-q³)/(1-q)
(1+q³)(1-q³)-4(1-q³)=0
(1-q³)(q²-3)=0
q³=1,q³=3
a4=a1q³
所以a4=1或3

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