Find the sum Sn of the first n terms of {an}, and you can find the following:

First find the sum of the first n terms whose general term is an-n.

Since the first term is a1-1= 2-1=1,the common ratio is 4.

So you can get the sum of the first n terms of this geometric series.

Add the first n terms with general terms n and n(n+ 1)/2.

Isn't it beautiful