设sn是等差数列{an}的前n项和,1/3S3与1/4S4的等比中项为1/5S5,1/3S3与1/4S4的等差中项为1,求通项an
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![设sn是等差数列{an}的前n项和,1/3S3与1/4S4的等比中项为1/5S5,1/3S3与1/4S4的等差中项为1,求通项an](/uploads/image/z/14578950-30-0.jpg?t=%E8%AE%BEsn%E6%98%AF%E7%AD%89%E5%B7%AE%E6%95%B0%E5%88%97%EF%BD%9Ban%EF%BD%9D%E7%9A%84%E5%89%8Dn%E9%A1%B9%E5%92%8C%2C1%2F3S3%E4%B8%8E1%2F4S4%E7%9A%84%E7%AD%89%E6%AF%94%E4%B8%AD%E9%A1%B9%E4%B8%BA1%2F5S5%2C1%2F3S3%E4%B8%8E1%2F4S4%E7%9A%84%E7%AD%89%E5%B7%AE%E4%B8%AD%E9%A1%B9%E4%B8%BA1%2C%E6%B1%82%E9%80%9A%E9%A1%B9an)
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设sn是等差数列{an}的前n项和,1/3S3与1/4S4的等比中项为1/5S5,1/3S3与1/4S4的等差中项为1,求通项an
设sn是等差数列{an}的前n项和,1/3S3与1/4S4的等比中项为1/5S5,1/3S3与1/4S4的等差中项为1,求通项an
设sn是等差数列{an}的前n项和,1/3S3与1/4S4的等比中项为1/5S5,1/3S3与1/4S4的等差中项为1,求通项an
S3=3a+3d
S4=4a+6d
S5=5a+10d
由题意得:1/3(3a+3d)*1/4(4a+6d)=[1/5(5a+10d)]^2
1/3(3a+3d)+1/4(4a+6d)=1*2
所以:a=4,d=-12/5
所以:an=4-12/5(n-1)
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