a3=1.5 S3=4.5 求a1和q 给过程

s3=a1+a2+a3=a1+a2+1.5=4.5

a1+a2=3 = a1(1+q), a1＝3/(1+q)

又 a1*q^2=a3=1.5, q^2/(1+q) =0.5, 2q^2 -q-1=0

(2q+1)(q-1)=0, q=-1/2 or q=1

若q＝1，a1＝a3＝1.5

若q＝-1/2, a1=a3/q^2 = 1.5*4=6

很明显q度等于1
a3=a1*q^2=1.5
s3=a1(1-q^3)/(1-q)
=a1*(1+q+q^2)=4.5
so
q^2/(1+q+q^2)=1.5/4.5=1/3
2q^2-q-1=0
（2q+1）(q-1)=0
q=-1/2,or q=1(舍)
a1=1.5/q^2=6

a3=a1q^2=1.5,a1=1.5/q^2
s3=a1(1+q+q^2)=4.5
a1(1+q)=4.5-a1q^2=3

1.5q^3+1.5q^2-3=0
q^3+q^2-2=0
(q-1)(q^2+2q+2)=0
q^2+2q+2=(q+1)^2+1>=1
q=1,
a1=1.5

a3=a1*q^2=1.5
s3=a1+a2+a3=a1(1+q+q^2)=4.5
解得q=1或-1/2
q=1时 a1=1.5
q=-1/2时，a1=6

s3=a1(1-q^3)/1-q=4.5
a3=a1q^2=1.5
解得