已知双曲线x^2/a2 - y^2/a^2 =1离心率，实轴长，虚轴长，焦距依次成等差数列，

x²/a²-y²/b²=1
离心率c/a,实轴2a,虚轴2b,焦距2c
设等差数列c/a,2a,2b,2c的公差为d
则有离心率c/a,实轴c/a+d,虚轴c/a+2d,焦距c/a+3d
即a=(c/a+d)/2,b=(c/a+2d)/2,c=(c/a+3d)/2
a²+b²=c²
[(c/a+d)/2]²+[(c/a+2d)/2]²=[(c/a+3d)/2]²
(c/a+d)²+(c/a+2d)²=(c/a+3d)²
c²/a²+2cd/a+d²+c²/a²+4cd/a+4d²=c²/a²+6cd/a+9d²
c²/a²=4d²
c/a=2d
离心率2d,实轴3d,虚轴4d,焦距5d
c/a=2d=5d/3d
d=5/6
a=3d=5/2
b=4d=10/3
a²=25/4
b²=100/9
该双曲线的方程为4x²/25-9y²/100=1