The nth term of the sequence 32 3 2 , 3, 7, 16, 35, 74, ..., is

The nth term of the sequence $\frac{3}{2}$, 3, 7, 16, 35, 74, ..., is

Answer Details

In the given sequence, each term is obtained by adding 1 to twice the previous term, starting from 32/3, which is the same as (96/3) + (32/3) = 128/3. So, the second term of the sequence is 2(128/3) + 1 = 257/3. Similarly, the third term is 2(257/3) + 1 = 515/3. Continuing this pattern, we can find the nth term by performing the following operation: Tn = 2(Tn-1) + 1 Therefore, the nth term of the sequence is 2^n * (128/3) - (2^n + 1)/3. Thus, the correct option is 5.2n - 2 - n.