Question

若an成等差数列,且a1,a3,a7,成等比数列,则（a1+a3)/(a2+a4)为多少?

Answer 1

∵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.