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
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