若an成等差数列,且a1,a3,a7,成等比数列,则（a1+a3)/(a2+a4)为多少?
问题描述：
若an成等差数列,且a1,a3,a7,成等比数列,则（a1+a3)/(a2+a4)为多少?
答
3/4
答
若an成等差数列，
a1,a2=a1+d,a3=a1+2d,a4=a1+3d,a5=a1+4d,a6=a1+5d,a7=a1+6d,...,
a1,a3,a7 成等比数列，
(a3)^2=(a1)(a7),
(a1+2d)^2=(a1)(a1+6d)=(a1)^2+6da1=(a1)^2+2da1+4d^2,
a1=d^2,
则 a2=a1+d=d^2+d,
a3=a1+2d=d^2+2d,
a4=a1+3d=d^2+3d,
(a1+a3)/(a2+a4)=
=(d^2+d^2+2d)/（d^2+d+d^2+3d)=
=(2d^2+2d)/(2d^2+4d)=
=(d+1)/(d+2),
d是等差数列的公差。
答
∵an成等差数列
∴a3=a1+2d,a7=a1+6d,
∵a1,a3,a7,成等比数列
∴a3^2=a1×a7
∴(a1+2d) ^2=a1×(a1+6d)
∴a1=2d(d≠0)或d=0
∴当d≠0时,
a1+a3=6d
a2+a4=8d
此时（a1+a3)/(a2+a4)=3/4
当d=0,无意义.