Write the first four terms of the sequence whose nth term is given
`(2^(n))/(n^(2))`

Answer

To find the first four terms of the sequence whose nth term is given by the formula \( t_n = \frac{2^n}{n^2} \), we will calculate the terms for \( n = 1, 2, 3, \) and \( 4 \).

### Step-by-step Solution:

1. **Calculate the first term \( t_1 \):**
\[ t_1 = \frac{2^1}{1^2} = \frac{2}{1} = 2 \]

2. **Calculate the second term \( t_2 \):**
\[ t_2 = \frac{2^2}{2^2} = \frac{4}{4} = 1 \]

3. **Calculate the third term \( t_3 \):**
\[ t_3 = \frac{2^3}{3^2} = \frac{8}{9} \]

4. **Calculate the fourth term \( t_4 \):**
\[ t_4 = \frac{2^4}{4^2} = \frac{16}{16} = 1 \]

### Summary of the First Four Terms:
The first four terms of the sequence are:
- \( t_1 = 2 \)
- \( t_2 = 1 \)
- \( t_3 = \frac{8}{9} \)
- \( t_4 = 1 \)

Thus, the first four terms of the sequence are \( 2, 1, \frac{8}{9}, 1 \).