Write first four terms of the A.P ., when the first term a and the common difference d are given as follow :
`a= - 1 , d = 1//2 `

Answer

To find the first four terms of the Arithmetic Progression (A.P.) given the first term \( a = -1 \) and the common difference \( d = \frac{1}{2} \), we can use the formula for the \( n \)-th term of an A.P.:

\[ A_n = a + (n - 1) \cdot d \]

### Step 1: Calculate the first term \( A_1 \)
Using the formula for the first term:
\[ A_1 = a + (1 - 1) \cdot d = -1 + 0 \cdot \frac{1}{2} = -1 \]

### Step 2: Calculate the second term \( A_2 \)
Using the formula for the second term:
\[ A_2 = a + (2 - 1) \cdot d = -1 + 1 \cdot \frac{1}{2} = -1 + \frac{1}{2} = -\frac{2}{2} + \frac{1}{2} = -\frac{1}{2} \]

### Step 3: Calculate the third term \( A_3 \)
Using the formula for the third term:
\[ A_3 = a + (3 - 1) \cdot d = -1 + 2 \cdot \frac{1}{2} = -1 + 1 = 0 \]

### Step 4: Calculate the fourth term \( A_4 \)
Using the formula for the fourth term:
\[ A_4 = a + (4 - 1) \cdot d = -1 + 3 \cdot \frac{1}{2} = -1 + \frac{3}{2} = -\frac{2}{2} + \frac{3}{2} = \frac{1}{2} \]

### Final Result
The first four terms of the A.P. are:
\[ A_1 = -1, \quad A_2 = -\frac{1}{2}, \quad A_3 = 0, \quad A_4 = \frac{1}{2} \]

### Summary
The first four terms of the A.P. are:
\[ -1, -\frac{1}{2}, 0, \frac{1}{2} \]