设数列{An}的前n项和为Sn若An+1=3Sn,a1=1则An=
问题描述：
设数列{An}的前n项和为Sn若An+1=3Sn,a1=1则An=
答
an+1=3Sn
an=3Sn-1
an=Sn-Sn-1=an+1/3-an/3
2an/3=an+1/3
q=an+1/an=2
a1=1
an=a12^(n-1)=2^(n-1)答案我知道，就是没过程。答案是an=1n=1 an=3×4^(n-2) n>1an+1=3Sn a2=3s1=3a1=3an=3Sn-1an=Sn-Sn-1=an+1/3-an/34an/3=an+1/3an+1/an=4a1=1,a2=3an=a2q^(n-2)=3*4^(n-2)