a2-a1=21,a3-a2=22,a4-a3=23,…依此类推可得an-an-1=2n-1
∴a2-a1+a3-a2+a4-a3…+an-an-1=an-a1=21+22+23+…+2n-1=2n-2
∴an-a1=2n-2,an=2n-1
故选C.