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

Answer

To find the first four terms of the sequence defined by the nth term \( t_n = (-1)^n \sin\left(\frac{n\pi}{2}\right) \), we will evaluate this expression for \( n = 1, 2, 3, \) and \( 4 \).

### Step-by-Step Solution:

1. **Calculate \( t_1 \)**:
\[ t_1 = (-1)^1 \sin\left(\frac{1\pi}{2}\right) \]
\[ t_1 = -1 \cdot \sin\left(\frac{\pi}{2}\right) \]
\[ t_1 = -1 \cdot 1 = -1 \]

2. **Calculate \( t_2 \)**:
\[ t_2 = (-1)^2 \sin\left(\frac{2\pi}{2}\right) \]
\[ t_2 = 1 \cdot \sin(\pi) \]
\[ t_2 = 1 \cdot 0 = 0 \]

3. **Calculate \( t_3 \)**:
\[ t_3 = (-1)^3 \sin\left(\frac{3\pi}{2}\right) \]
\[ t_3 = -1 \cdot \sin\left(\frac{3\pi}{2}\right) \]
\[ t_3 = -1 \cdot (-1) = 1 \]

4. **Calculate \( t_4 \)**:
\[ t_4 = (-1)^4 \sin\left(\frac{4\pi}{2}\right) \]
\[ t_4 = 1 \cdot \sin(2\pi) \]
\[ t_4 = 1 \cdot 0 = 0 \]

### Summary of the First Four Terms:
The first four terms of the sequence are:
\[ t_1 = -1, \quad t_2 = 0, \quad t_3 = 1, \quad t_4 = 0 \]
Thus, the first four terms of the sequence are:
\[ \{-1, 0, 1, 0\} \]