Question

在等比数列An中a3等于3/2,S3等于9/2，求a1和q

Answer 1

a3=a1*q^2=3/2
s3=a1*(1+q+q^2)=9/2
两个相除
1+q+q^2=3q^2
1+q=2q^2
q=1或者-1/2
若q=1
a1=3/2,
若q=-1/2
a1=6

Answer 2

解：3/2=a3=q^2*a1
9/2=S3=a1+a2+a3=a1+q*a1+3/2
故3q^2=（9/2-3/2）*q^2=(a1+q*a1+3/2-3/2)*q^2
=a1*q^2+a1*q^2*q
=3/2+(3/2)q
解之得
q=1或(-1/2)
若q=1则a1=a3/(q^2)=a3=3/2
若q=（-1/2）则a1=a3/(q^2)=a3=6

Answer 3

设a1=a，则a3=a*q*q=3/2,a+a*q+a*q*q=9/2,所以：a1=3/2 q=1;a=6 q=-1/2;