设a1 d 为首项及公差
a4^2-a2^2+a5^2-a3^2=0
(a4-a2)(a4+a2)+(a5-a3)(a5+a3)=0
(2d)(2a1+4d)+(2d)(2a1+6d)=0
2d(4a1+10d)=0
d(2a1+5d)=0
得d=0或 2a1+5d=0 ...(1)
s7=7a1+(1+2+3+4+5+6)d=7a1+21d=7
a1+3d=1 .(2)
(1)(2)得 d=2
a1=-5
an=-5+(n-1)*2 =2n-7
Sn=na1+(1+n-1)*(n-1)/2 *2=-5n+n(n-1)=-5n+n^2-n=n^2-6n