a1+a2+a3+a4=240
a1+a1*q+a1*q^2+a1*q^3
=a1(q^3+q^2+q+1)
=a1[q^2(q+1)+(q+1)]
=a1(q^2+1)(q+1)
=240
a2+a4=180
a1*q+a1*q^3
=a1(q^3+q)
=a1*q*(q^2+1)
=180
两式相除得：
[a1(q^2+1)(q+1)]/[a1*q*(q^2+1)]
=(q+1)/q
=4/3
得q=3
将q=3代入a2+a4=180,得：
a1*3+a1*3^3=180
30a1=180
a1=6,得解.