Question 826461
{{{U[n]=2^T[n]=2^(a+(n-1)*d)}}}


{{{U[n]=2^a*2^((n-1)*d)=(2^(a-d))*2^(n*d)
}}}

take integer k, then

{{{U[k+1]=2^a*2^(k*d)}}}


{{{U[k]=2^a*2^((k-1)*d)}}}


the ratio is

{{{U[k+1]/U[k]=2^((a+kd)-(a-d+kd))=2^d}}}

therefore it is geometric with

{{{a[0]=2^(a-d)}}}   and {{{r=2^d}}}