等比数列{an}的前n项和为sn,a2=6,s3=21,则公比q=
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![等比数列{an}的前n项和为sn,a2=6,s3=21,则公比q=](/uploads/image/z/10353674-2-4.jpg?t=%E7%AD%89%E6%AF%94%E6%95%B0%E5%88%97%7Ban%7D%E7%9A%84%E5%89%8Dn%E9%A1%B9%E5%92%8C%E4%B8%BAsn%2Ca2%3D6%2Cs3%3D21%2C%E5%88%99%E5%85%AC%E6%AF%94q%3D)
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