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一道等比数列题a3=3/2s3=9/2求a1与q
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一道等比数列题
a3=3/2 s3=9/2 求a1与q
a3=3/2 s3=9/2 求a1与q
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答案和解析
S3=a1+a1q+3/2=9/2,a1+a1q=3
a1(1+q)=3,a1=3/(1+q).(1)
a3=a1q^2=3/2.(2)
(1)代入(2):
3q^2/(1+q)=3/2,6q^2=3+3q,6q^2-3q-3=0,
2q^2-q-1=0,(q-1)(2q+1)=0,∴q=1或q=-1/2代入(2)
a1q^2=3/2,得a1=3/2或a1=6
∴a1=3/2,q=1或a1=6,q=-1/2
a1(1+q)=3,a1=3/(1+q).(1)
a3=a1q^2=3/2.(2)
(1)代入(2):
3q^2/(1+q)=3/2,6q^2=3+3q,6q^2-3q-3=0,
2q^2-q-1=0,(q-1)(2q+1)=0,∴q=1或q=-1/2代入(2)
a1q^2=3/2,得a1=3/2或a1=6
∴a1=3/2,q=1或a1=6,q=-1/2
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