Question

在等比数列里已知a3=3/2,S3=9/2,求a1和q

Answer 1

a1*q^2=a3=3/2a1(1-q^3)/(1-q)=S3=9/2粮食相除q^2(1-q)/(1-q^3)=1/33q^2(1-q)=(1-q^3)2q^3-3q^2+1=02q^2(q-1)-(q-1)(q+1)=0,而q≠12q^2-q-1=0(2q+1)(q-1)=0,而q≠12q+1=0,q=-1/2a1=a3/q^2=6故a1=6 ,q=-1/2