an=n(n+1)/2
3(a1+a2+……+an)=(n+2)an
3Sn = (n+2)an .(1)
3S(n-1) = (n + 1)a(n-1).(2)
(1)-(2)得：
3an = (n+2)an - (n + 1)a(n-1)
(n-1)an = (n + 1)a(n-1)
an/a(n-1) = (n + 1)/(n-1)
然后用你们肯定学过的累乘法：
（a2/a1)(a3/a2)(a4/a3).[a(n-1)/a(n-2)][an/a(n-1)] = (3/1)(4/2)(5/3).[n/(n-2)][(n+1)/(n-1)]
an/a1 = n(n+1)/2
因为a1=1
所以,an = n(n+1)/2