n=1时,
2a1-a1=S1S1=a1²
a1²-a1=0
a1(a1-1)=0
a1=0或a1=1
(1)
a1=0时,2an-a1=S1Sn=a1Sn
2an=0
an=0,数列{an}是各项均为0的常数数列,a7=0
(2)
a1=1时,2an-a1=S1Sn=a1Sn
Sn=2an-1
n≥2时,an=Sn-S(n-1)=2an -1-[2a(n-1)-1]
an=2a(n-1)
an/a(n-1)=2,为定值,又a1=1,数列{an}是以1为首项,2为公比的等比数列.
an=1×2^(n-1)=2^(n-1)
a7=2^(7-1)=2^6=64