Question

数学:已知公差不为0的等差数列{An}的首项A1=1,前n项和为Sn,若数列{Sn/An}是等差数列,求An?

Answer 1

S1/a1=1
S2/a2-S1/a1=(2+d)/(1+d)-1=d/(1+d)
S3/a3-S1/a1==(3+3d)/(1+2d)-1=(2+d)/(1+2d)

2*d/(1+d)=(2+d)/(1+2d)
解得d=1，d=0(舍去)
所以，an=n

Answer 2

S1/a1=1
S2/a2-S1/a1=d/(1+d)=D (1)
S3/a3-S1/a1=(2+d)/(1+2d)=2D (2)
S4/a4-S1/a1=(3+d)/(1+3d)=3D (3)
(1)、（2）解得d=1，d=-2/3
（1）、（3）解得 d=1，d=-3/4
所以 d=1
所以，an=n