等比数列{an}的前n项和为sn,a2=6,s3=21,则公比q=

等比数列{an}的前n项和为sn,a2=6,s3=21,则公比q=
等比数列{an}的前n项和为sn,a2=6,s3=21,则公比q=

等比数列{an}的前n项和为sn,a2=6,s3=21,则公比q=
S3=a1+a2+a3=a1+a1*q+a1*q*q=21
a2=a1*q=6,即a1=6/q,代回上式,
得6/q + 6 + 6q = 21
接方程q=2或者1/2两个值,验证下都成立

s3=a1+a2+a3=a1+6+a2*q=a1+6+6q=21 => a1+6q=15 => a1=15-6q
a2=a1*q=6
(15-6q)q=6 解得q=1/2或q=2