Write the first four terms of the sequence whose nth term is given
`(n^(2)+1)/(n)`

Answer

To find the first four terms of the sequence whose nth term is given by the formula \( t_n = \frac{n^2 + 1}{n} \), we will substitute the values of \( n \) from 1 to 4 into the formula.

### Step-by-Step Solution:

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

2. **Calculate \( t_2 \)**:
\[ t_2 = \frac{2^2 + 1}{2} = \frac{4 + 1}{2} = \frac{5}{2} \]

3. **Calculate \( t_3 \)**:
\[ t_3 = \frac{3^2 + 1}{3} = \frac{9 + 1}{3} = \frac{10}{3} \]

4. **Calculate \( t_4 \)**:
\[ t_4 = \frac{4^2 + 1}{4} = \frac{16 + 1}{4} = \frac{17}{4} \]

### Summary of the First Four Terms:
- \( t_1 = 2 \)
- \( t_2 = \frac{5}{2} \)
- \( t_3 = \frac{10}{3} \)
- \( t_4 = \frac{17}{4} \)

Thus, the first four terms of the sequence are:
\[ 2, \frac{5}{2}, \frac{10}{3}, \frac{17}{4} \]