设Sn是等差数列{an}的前n项和,已知1/3S3,1/4S4的等比中项为1/5S5,1/5S5与1/4S4的等差中项为1,求an

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设Sn是等差数列{an}的前n项和,已知1/3S3,1/4S4的等比中项为1/5S5,1/5S5与1/4S4的等差中项为1,求an
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设Sn是等差数列{an}的前n项和,已知1/3S3,1/4S4的等比中项为1/5S5,1/5S5与1/4S4的等差中项为1,求an
设Sn是等差数列{an}的前n项和,已知1/3S3,1/4S4的等比中项为1/5S5,1/5S5与1/4S4的等差中项为1,求an

设Sn是等差数列{an}的前n项和,已知1/3S3,1/4S4的等比中项为1/5S5,1/5S5与1/4S4的等差中项为1,求an
设等差数列的首项为a1,公差为d.
则S3=3a1+3×2d/2=3a1+3d.
S4=4a1+4×3d/2=4a1+6d.
S5=5a1+5×4d/2=5a1+10d.
∵1/3S3,1/4S4的等比中项为1/5S5,
∴1/3(3a1+3d)•1/4(4a1+6d)=[1/5(5a1+10d)]²……①
∵1/5S5与1/4S4的等差中项为1,
∴1/5(5a1+10d)+ 1/4(4a1+6d)=2……②
解得d=0,a1=1或d=12,a1=-20.
∴an=1或an=-20+12(n-1)=12n-32.

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