设数列{an}是公差不为零的等差公式,Sn是数列{an}的前n项和,且S3的平方=9S2,S4=4S2,求数列{an}的通项公式.

d=a4-a3=(s4-s3)-(s3-s2)=s4+s2=5s2=5(a1+a2)=10a1+5d

10a1+4d=0

(s3)^2=(3a1+3d)^2=9*(2a1+d)
(a1+d)^2=2a1+d

a1^2+d^2+2a1d-2a1-d=0

a1=4/9, d=8/9

S3=3a1+3*2/2*d
S2=2a1+2*1/2*d
S3^=9S2
a1^+d^+2a1d=2a1+d
S4=4a1+4*3/2*d=8a1+4d=4a1+6d
SO: 4a1=2d SO: d=2a1
SO:a1^+4a1^+4a1^=2a1+2a1
SO:9a1^-4a1=0

SO:a1(9a1-4)=0
SO: a1=0 or a1=4/9
SO:d=0 or d=8/9 Because d<>0,So d=8/9.

SO: An=4/9+(n-1)8/9=(8/9)n-4/9