a[n+ 1]+ 1 = 2(an+ 1)

(a[n+ 1]+ 1)/(an+ 1)= 2

So the sequence {an+ 1} is a geometric series.

an+ 1=(a 1+ 1)q^(n- 1)=2*2^(n- 1)=2^n

an=2^n- 1