Question

在等比数列{an }中,已知S3=9/2 a3=3/2 求a1与q

Answer 1

S3=a1+a2+a3=a1+a1q+a1q^2=a1(1+q+q^2)=9/2 (1)

a3=a1q^2=3/2 (2)

(1)/(2) 2q^2-q-1=0 (q-1)(q+1/2)=0 q=1 或 q=-1/2

当q=1 时,a1=3/2

当q=-1/2 时,a1=6