Question

数列{an}的前n项和为Sn,Sn=1/3(an-1).求an的通项公式及S10

Answer 1

∵Sn=1/3(An-1)

∴Sn-1=1/3(An-1 -1)

∴An=Sn-Sn-1=1/3(An-1)-1/3(An-1 -1)

化简得2/3An=-1/3An-1

即An/An-1=-1/2=q

∴数列为等比数列

a1=1/3(a1-1)

a1=-1/2.

所以an=(-1/2)*(-1/2)^(n-1)

S10=(-1/2)*(1-(-1/2)^10)/(1+1/2)=341/1024