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)=?
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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)=?
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)=?
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)=?
a1=a1
a3=a1+2d
a9=a1+8d
a3*a3=a1*a9
(a1+2d)^2=a1*(a1+8d)
a1^2+4d^2+4a1*d=a1^2+8a1*d
==> a1=d
(a1+a3+a9)/(a2+a4+a10)
=[a1+ (a1+2d)+(a1+8d)] / [(a1+d)+(a1+3d)+(a1+9d)]
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a1=a1
a3=a1+2d
a9=a1+8d
a3*a3=a1*a9
(a1+2d)^2=a1*(a1+8d)
a1^2+4d^2+4a1*d=a1^2+8a1*d
==> a1=d
(a1+a3+a9)/(a2+a4+a10)
=[a1+ (a1+2d)+(a1+8d)] / [(a1+d)+(a1+3d)+(a1+9d)]
=[3a1+10d]/[3a1+13d]
=[13d]/[16d]
=13/16
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a1,a3,a9成等比数列
有a3*a3=a1*a9,即
(a1+2d)^2=a1*(a1+8d)
括号打开化简的4d*d=4a1*d
有a1=d
(a1+a3+a9)/(a2+a4+a10)=(3a1+10d)/(3a1+13d)=13/16
谢谢,祝你学习进步!为何不采纳我的。。。为何不采纳我的。。。下次采纳你。因为回答太多了!好吧,记住我啊!好...
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a1,a3,a9成等比数列
有a3*a3=a1*a9,即
(a1+2d)^2=a1*(a1+8d)
括号打开化简的4d*d=4a1*d
有a1=d
(a1+a3+a9)/(a2+a4+a10)=(3a1+10d)/(3a1+13d)=13/16
谢谢,祝你学习进步!
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