等比数列{an}前n项和为Sn,若S3=2a3,则公比q=

问题描述:

等比数列{an}前n项和为Sn,若S3=2a3,则公比q=

grg

S3=a1+a2+a3=2a3
则a1+a2=a3
则a1+a1*q=a1*q²
两边约去a1
则 1+q=q²
q=


S3=2a3
a1+a2+a3=2a3
a1(1+q+q²)=2a1*q²
q²-q-1=0
q=(1±√5)/2