已知等差数列{An}的公差d不等于0,且A1,A3,A9成等比数列,则(A1+A3+A9)/(A2+A4+A10)=多少?答案是13/16
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![已知等差数列{An}的公差d不等于0,且A1,A3,A9成等比数列,则(A1+A3+A9)/(A2+A4+A10)=多少?答案是13/16](/uploads/image/z/1159560-0-0.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%AEd%E4%B8%8D%E7%AD%89%E4%BA%8E0%2C%E4%B8%94A1%2CA3%2CA9%E6%88%90%E7%AD%89%E6%AF%94%E6%95%B0%E5%88%97%2C%E5%88%99%EF%BC%88A1%2BA3%2BA9%EF%BC%89%2F%EF%BC%88A2%2BA4%2BA10%EF%BC%89%3D%E5%A4%9A%E5%B0%91%3F%E7%AD%94%E6%A1%88%E6%98%AF13%2F16)
已知等差数列{An}的公差d不等于0,且A1,A3,A9成等比数列,则(A1+A3+A9)/(A2+A4+A10)=多少?答案是13/16
已知等差数列{An}的公差d不等于0,且A1,A3,A9成等比数列,则(A1+A3+A9)/(A2+A4+A10)=多少?
答案是13/16
已知等差数列{An}的公差d不等于0,且A1,A3,A9成等比数列,则(A1+A3+A9)/(A2+A4+A10)=多少?答案是13/16
a3=a1+2d
q9=a1+8d
a1,a3,a9成等比数列
所以(a1+2d)^2=a1*(a1+8d)
a1^2+4a1d+4d^2=a1^2+8a1d
d^2=a1d
d≠0
d=a1
所以a1+a3+a9=a1+(a1+2d)+(a1+8d)=a1+3a1+9a1=13a1
a2+a4+a10=(a1+d)+(a1+3d)+(a1+9d)=2a1+4a1+10a1=16a1
所以(a1+a3+a9)/(a2+a4+a10)=13/16
解:设an的公差是d
∴a3=a1+2d,a9=a1+8d
a2=a1+d,a4=a1+3d,a10=a1+9d
∴a1+a3+a9=3a1+10d,a2+a4+a10=3a1+13d
∵a1,a3,a9依次成等比数列
∴a3/a1=a9/a3
∴a1^2+4d^2+4a1d=a1^2+8a1d
∴a1=d
∴(a1+a3+a9)/(a2+a4+a10)=(3a1+10d)/(3a1+13d)=13d/16d=13/16
A3*A3=A1*A9
(A1+2D)*(A1+2D)=A1*(A1+8D)
D=A1
(A1+A3+A9)/(A2+A4+A10)
=(A1+A1+2D+A1+8D)/(A1+D+A1+3D+A1+9D)
=(3A1+10D)/(3A1+13D)
=13/16