已知数列﹛an﹜的前n项和为Sn,且有a1=3,4Sn=6an-an-1+4Sn-1,则an=

Question

已知数列﹛an﹜的前n项和为Sn,且有a1=3,4Sn=6an-an-1+4Sn-1,则an=

Answer 1

∵4Sn=6an-an-1+4Sn-1
∴4[Sn-S(n-1)]=6an-a(n-1)
∴4an=6an-a(n-1)
∴2an=a(n-1)
an/a(n-1)=1/2
∴{an}为等比数列,公比为1/2
∴an=3×(1/2)^(n-1)