等差数列an的公差和等比数列bn的公比相等,且都等于d(d>0）d不等于0,若a1=b1,a3=5b3,a5=5b5求a

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等差数列an的公差和等比数列bn的公比相等,且都等于d(d>0）d不等于0,若a1=b1,a3=5b3,a5=5b5求an,bn

设an=a1+(n-1)d,bn=b1d^(n-1)=a1d^(n-1)
a3=a1+2d,
b3=a1d^2
a5=a1+4d,
b5=a1d^4
a1+2d=5a1d^2
a1+4d=5a1d^4
d^2=1+(2/5)√5
d=√[1+(2/5)√5]
a1=2d/(5d^2-1)=2√[1+(2/5)√5]/{5[1+(2/5)√5]-1}
=2√[5+2√5]/[10+4√5]
=1/√(5+2√5)

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