(5n-8)S(n+1)-(5n+2)Sn=-20n-8(5n-8)an+(5n-8)Sn-(5n+2)Sn=-20n-8(5n-8)an-10Sn=-20n-8①令n=n-1,得(5n-13)a(n-1)-10S(n-1)=-20n+12②①-②,得(5n-18)an-(5n-13)a(n-1)=-20③再令n=n-1,得(5n-23)a(n-1)-(5n-18)a(n-2)=-20④③-④,得(5n-18)an+(5n-18)a(n-2)=(5n-13)a(n-1)+(5n-23)a(n-1)=2(5n-18)a(n-1)得an+a(n-2)=2a(n-1)an-a(n-1)=a(n-1)-a(n-2)所以an是等差数列!正毕!