Question

设数列{An}的前n项和为Sn若An+1=3Sn,a1=1则An=

Answer 1

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)

追问

答案我知道，就是没过程。答案是an=1 n=1
an=3×4^(n-2) n>1

追答

an+1=3Sn a2=3s1=3a1=3
an=3Sn-1
an=Sn-Sn-1=an+1/3-an/3
4an/3=an+1/3
an+1/an=4
a1=1,a2=3
an=a2q^(n-2)=3*4^(n-2)

Answer 2

a(n+1)=3Sn
S(n+1)-Sn=3Sn
S(n+1)=4Sn
{Sn}为等比数列
Sn=S1*q^(n-1)=1*4^(n-1)
an=Sn-S(n-1)=3*4^(n-2)