设Sn是等差数列｛an｝的前n项和,若S8/S4 =3,则S16/S8等于多少,为什么

根据等差数列的规律来求 Sn,S2n-Sn,S3n-S2n,……是等差数列 故S4,S8-S4,S12-S8,S16-S12成等差数列 2(S8-S4)=S4+S12-S8 2S8-2S4=S4+S12-S8 S12=3S8-3S4 2(S12-S8)=S8-S4+S16-S12 3S12=3S8-S4+S16=9S8-9S4 6S8=S16+8S4 因为S8=3S4 所以6S8=S16+8S8/3 18S8=3S16+8S8 10S8=3S16 S16/S8=10/3 所以