设数列满足 {an} 满足 a1=0 ,an+1 -2a n=1, 则 a 100 = ()

A、2^99-1
B、2^99
C、2^99+1
D、2^100-1
E、2^100+1
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正确答案:

A

答案解析:

构造等比数列:an+1-2an=1,有an+1=2an+1,令an+1+t=2(2an+t)→an+1=2an+t,所以t=1,所以an+1+1=2(an+1),所以an+1是以a1+1=1为首项,公比为2的等比数列,所以an=2n-1-1,an=299-1,选A。

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