等差数列｛an}的公差d不等于0,且a1,a2,a3成等比数列,求（a1+a3+a9)/(a2+a4+a10)的值.为什么(a1+2d)^2=a1*(a1+8d)
问题描述：
等差数列｛an}的公差d不等于0,且a1,a2,a3成等比数列,求（a1+a3+a9)/(a2+a4+a10)的值.
为什么(a1+2d)^2=a1*(a1+8d)
答
a3=a1+2d
a9=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
因为两边之积等于中间项的平方
答
13\16
答
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