设公比为q.
q=1时,sn=n,s4+s5+s6=4+5+6=156,不符.
q1时：
s3=a1(1-q^3)/(1-q)=3
s4+s5+s6=a1(1-q^4+1-q^5+1-q^6)/(1-q)=a1(3-q^4-q^5-q^6)/(1-q)=6
两式相除得：(3-q^4-q^5-q^6)/(1-q^3)=2
即：
q^6+q^5+q^4-2q^3-1=0
q^6-q^5+2q^5-2q^4+3q^4-3q^3+q^3-1=0
(q-1)(q^5+2q^4+3q^3+q^2+q+1)=0
(q^5+2q^4+3q^3+q^2+q+1)=0
解得唯一实根q=-0.728676677160428
a1=3(1-q)/(1-q^3)=3.739282176466450