已知a3=3/2,S3=9/2,求a1与q.

已知a3=3/2,S3=9/2,求a1与q.
已知a3=3/2,S3=9/2,求a1与q.

已知a3=3/2,S3=9/2,求a1与q.
S3=a1(1-q^3)/(1-q)=9/2
a3=a1q^2=3/2
两式相除得
[(1-q^3)/(1-q)]/q^2=3
[(1-q)(1+q+q^2)/(1-q)]/q^2=3
(1+q+q^2)/q^2=3
1+q+q^2=3q^2
2q^2-q-1=0
(2q+1)(q-1)=0
q=-1/2或q=1
当q=-1/2时
a3=a1q^2
3/2=a1*(-1/2)^2
a1=6
当q=1时
a3=a1q^2
3/2=a1*1^2
a1=3/2