已知{an}是等比数列,且a1a9=64,a3+a7=20,求a11 .

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已知{an}是等比数列,且a1a9=64,a3+a7=20,求a11 .
已知{an}是等比数列,且a1a9=64,a3+a7=20,求a11 .

已知{an}是等比数列,且a1a9=64,a3+a7=20,求a11 .
已知{an}是等比数列,则a1a9=a3a7=64
又a3+a7=20
则a3,a7分别为4,16
若a3=4,a7=16,则q^4=a7/a3=4
a11=a7*q^4=64
若a3=16,a7=4,则q^4=a7/a3=1/4
a11=a7*q^4=1

a1a9=64,a3+a7=20,求a11
a9=a1*q^8
a1a9=a1^2*q^8=64
a3=a1q^2
a7=a1q^6
a3+a7=a1(q^2 +q^6)=20
a1=20/(q^2 +q^6)
(400/(q^2 +q^6) ^2)* q^8=64
(q^4+2q^8+q^12)/ q^8=400/64
q...

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a1a9=64,a3+a7=20,求a11
a9=a1*q^8
a1a9=a1^2*q^8=64
a3=a1q^2
a7=a1q^6
a3+a7=a1(q^2 +q^6)=20
a1=20/(q^2 +q^6)
(400/(q^2 +q^6) ^2)* q^8=64
(q^4+2q^8+q^12)/ q^8=400/64
q^4+1/q^4=4.25
q^8-4.25q^4+1
q^4=0.25和8
a1^2*q^8=64
a1=(64/q^8)=8/q^4
解得a1=32 (q^4=0.25) 和1 (q^4=4)
a11=a1*q^10=a1(q^4)^2.5
解得
a11=1 (a1=32 q^4=0.25)和32 (a1=1 q^4=4)

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