Sequence 3 / 2,17 / 4,57 / 8161 / 16. The first n terms and Sn

Sequence 3 / 2,17 / 4,57 / 8161 / 16. The first n terms and Sn

3 / 2,17 / 4,57 / 8161 / 16. Transform, 1 + 1 / 2,4 + 1 / 4,7 + 1 / 8,10 + 1 / 16. It can be seen that the sequence is composed of an arithmetic sequence and an arithmetic sequence
The arithmetic sequence: 1,4,7,10,. D = 3, A1 = 1, then an = a1 + (n-1) d = 3n-2, Sn = Na1 + n (n-1) d / 2 = (3N ^ 2) / 2-N / 2
If the number sequence is 1 / 2, 1 / 4, 1 / 8, 1 / 16,. Q = 1 / 2, A1 = 1 / 2, then an = a1q ^ ((n-1)) = [1 / 2] ^ n, Sn = (A1 (1-Q ^ n)) / (1-Q) = 1 - [1 / 2] ^ n
So the general formula of the sequence is an = 3n-2 + [1 / 2] ^ n, and the sum of the first n terms is Sn = (3N ^ 2) / 2-N / 2 + 1 - [1 / 2] ^ n