设等比数列{an}的前n项和为sn,若S6,S9,S3成等差数列,问2S3,S6,S12-S6S能否成等比数列?请说明理由.S12-S6S改为S12-S6
来源:学生作业帮助网 编辑:作业帮 时间:2024/07/21 04:12:23
![设等比数列{an}的前n项和为sn,若S6,S9,S3成等差数列,问2S3,S6,S12-S6S能否成等比数列?请说明理由.S12-S6S改为S12-S6](/uploads/image/z/14573971-19-1.jpg?t=%E8%AE%BE%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%2C%E8%8B%A5S6%2CS9%2CS3%E6%88%90%E7%AD%89%E5%B7%AE%E6%95%B0%E5%88%97%2C%E9%97%AE2S3%2CS6%2CS12-S6S%E8%83%BD%E5%90%A6%E6%88%90%E7%AD%89%E6%AF%94%E6%95%B0%E5%88%97%3F%E8%AF%B7%E8%AF%B4%E6%98%8E%E7%90%86%E7%94%B1.S12-S6S%E6%94%B9%E4%B8%BAS12-S6)
x){nOy6uӎՉyg<{pI=Ov*yѽ4L'R'YA4輜(X$mhly ڿX-f=|F=gSvmpl=`˱9Jf@-{d7%ƶF@Qvvava1gkckYhXqƶ
@gki@D60j3yd⧭Kn~ڿF 1 m:
设等比数列{an}的前n项和为sn,若S6,S9,S3成等差数列,问2S3,S6,S12-S6S能否成等比数列?请说明理由.S12-S6S改为S12-S6
设等比数列{an}的前n项和为sn,若S6,S9,S3成等差数列,问2S3,S6,S12-S6S能否成等比数列?请说明理由.
S12-S6S改为S12-S6
设等比数列{an}的前n项和为sn,若S6,S9,S3成等差数列,问2S3,S6,S12-S6S能否成等比数列?请说明理由.S12-S6S改为S12-S6
因为S6,S9,S3成等差数列所以S6+S3=2S9,所以2a1(1+q+q^2)+a1q3(1+q+q^2)=2a(1+q+q^2+.q^8)解得q^3=-1 2S3*(S12-S6)=2a1(1+q+q^2)+aq^6(1+q+...q^5),把q^3=-1代入即可