设Sn是等差数列an的前n项和,且(1/3)S3与(1/4)S4的等比中项为(1/5)S5,(1/3)S3与(1/4)S4的等差中项设Sn是等差数列an的前n项和,且(1/3)S3与(1/4)S4的等比中项为(1/5)S5,(1/3)S3与(1/4)S4的等

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设Sn是等差数列an的前n项和,且(1/3)S3与(1/4)S4的等比中项为(1/5)S5,(1/3)S3与(1/4)S4的等差中项设Sn是等差数列an的前n项和,且(1/3)S3与(1/4)S4的等

设Sn是等差数列an的前n项和,且(1/3)S3与(1/4)S4的等比中项为(1/5)S5,(1/3)S3与(1/4)S4的等差中项设Sn是等差数列an的前n项和,且(1/3)S3与(1/4)S4的等比中项为(1/5)S5,(1/3)S3与(1/4)S4的等
设Sn是等差数列an的前n项和,且(1/3)S3与(1/4)S4的等比中项为(1/5)S5,(1/3)S3与(1/4)S4的等差中项
设Sn是等差数列an的前n项和,且(1/3)S3与(1/4)S4的等比中项为(1/5)S5,(1/3)S3与(1/4)S4的等差中项为1,求等差数列的通项公式an

设Sn是等差数列an的前n项和,且(1/3)S3与(1/4)S4的等比中项为(1/5)S5,(1/3)S3与(1/4)S4的等差中项设Sn是等差数列an的前n项和,且(1/3)S3与(1/4)S4的等比中项为(1/5)S5,(1/3)S3与(1/4)S4的等
设an=a1+(n-1)d S3=a1+a2+a3 (1/3)S3=a1+d
(1/4)S4=a1+(3\2)d
(1\5)S5=a1+2d
(1/3)S3+(1/4)S4=2a1+5\2d=2 (1/3)S3*(1/4)S4=(1\5)S5*(1\5)
解得a1=4\7 d=12\35 所以an=12\35n+8\35

S3=(a1+a3)x3/2 1/3S3=(a1+a3)x/2
1/4S4=(a1+a4)x/2
1/3S3 x 1/4S4=(2a1+2d)(2a1+3d)/2=1/5S5=(2a1+4d)平方
所以10d*2+6a1d=0
所以10d=-6a1 所以5d=-3a1
1/3S3 + 1/4S4=4a1+5d/2=a1/2=1/2S1

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