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=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,bna3=a1+2
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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=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,bna3=a1+2](/uploads/image/z/3957136-16-6.jpg?t=%E5%B7%B2%E7%9F%A5%E7%AD%89%E5%B7%AE%E6%95%B0%E5%88%97%7Ban%7D%E7%9A%84%E5%85%AC%E5%B7%AE%E4%B8%8E%E7%AD%89%E6%AF%94%E6%95%B0%E5%88%97%7Bbn%7D%E7%9A%84%E5%85%AC%E6%AF%94%E7%9B%B8%E7%AD%89%2C%E4%B8%94%E9%83%BD%E7%AD%89%E4%BA%8Ed%28d%3E0%2C%E4%B8%94d%E2%89%A01%29%2C%E5%8F%88%E7%9F%A5a1%3D%E5%B7%B2%E7%9F%A5%E7%AD%89%E5%B7%AE%E6%95%B0%E5%88%97%EF%BD%9Ban%EF%BD%9D%E7%9A%84%E5%85%AC%E5%B7%AE%E4%B8%8E%E7%AD%89%E6%AF%94%E6%95%B0%E5%88%97%EF%BD%9Bbn%EF%BD%9D%E7%9A%84%E5%85%AC%E6%AF%94%E7%9B%B8%E7%AD%89%2C%E4%B8%94%E9%83%BD%E7%AD%89%E4%BA%8Ed%EF%BC%88d%3E0%2C%E4%B8%94d%E2%89%A01%EF%BC%89%2C%E5%8F%88%E7%9F%A5a1%3Db1%2Ca3%3D3b3%2Ca5%3D5b5%2C%E6%B1%82an%2Cbna3%3Da1%2B2)
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=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,bna3=a1+2
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=
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
接下来该怎么解呢
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=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,bna3=a1+2
a3=3b3
a1+2d=3a1d²
(3d²-1)a1=2d
a1=2d/(3d² -1)
a5=5b5
a1+4d=5a1d⁴
(5d⁴-1)a1=4d
a1=4d/(5d⁴-1)
2d/(3d²-1)=4d/(5d⁴-1)
5d⁴-6d²+1=0
(d-1)(5d-1)=0
d=1(d≠1,舍去)或d=1/5
a1=2d/(3d² -1)=2/(3d -1/d)=2/(3/5 -5)=-5/11
an=a1+(n-1)d=-5/11 +(1/5)(n-1)=-36/55 +n/5
bn=b1d^(n-1)=(-5/11)×(1/5)^(n-1)=-1/[11×5^(n-2)]