作业帮已知等差数列｛an｝的公差与等比数列｛bn｝的公比相等,且都等于d（d>0,且d≠1）,又知a1=b1,a3=3b3,a
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已知等差数列｛an｝的公差与等比数列｛bn｝的公比相等,且都等于d（d>0,且d≠1）,又知a1=b1,a3=3b3,a5=5b5,求an,bn
a3=a1+2d a5=a1+4d
b3=b1*d^2 b5=b1*d^4
a1+2d=b1*d^2 a1+4d=5b1*d^4
2d=3a1*d^2-a1 (1) 4d=a1*d^4-a1 (2)
(2)/(1)
2=(5d^4-1)/(3d^2-1)
5d^4-6d^2+1=0
d^2=1 (舍去) d^2=1/5
d=√5/5 a1=-√5
an=-√5+(n-1)*√5/5
bn=-√5*(√5/5)^(n-1)
b3=b1*d^2 b5=b1*d^4
a1+2d=b1*d^2 a1+4d=5b1*d^4
2d=3a1*d^2-a1 (1) 4d=a1*d^4-a1 (2)
(2)/(1)
2=(5d^4-1)/(3d^2-1)
5d^4-6d^2+1=0
d^2=1 (舍去) d^2=1/5
d=√5/5 a1=-√5
an=-√5+(n-1)*√5/5
bn=-√5*(√5/5)^(n-1)
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