A0=1,An-1=5An-1 for n>=1 the remainder when A2011 is divided by 13 is??

hence

now

now expanding (26-1)^1006 we get all the terms to be divisible by 26, and hence by 13 except the last term which is 1
and hence when 1 is subtracted from the expansin all the remaining terms are divisible by 13 and hence the remainder is
0