Question

已知数列{a n}的前n项和为S n,且a1=1,a (n+1)=1/3 S n,求：（1）a2,a3,a4的值及数列{

Answer 1

since a(n+1)=1/3 S n

then,Sn+1=4/3Sn

S1=a1=1,so,Sn=(4/3)^(n-1)

so,an=1/3 S (n-1)=(1/3)*(4/3)^(n-2)

a2=1/3,a3=4/9,a4=16/27

an=4^(n-2)/3^(n-1)

a2+a4+a6+……+a2n=(4/3)*[(16/9)^n-1]/(16/9-1)=(12/7)*(4/3)^2n-12/7