Write first four terms of the A.P., when the first term 'a' and the common difference 'd' are given as follows :
(i) a=5, d=3 (ii) a=-2, d=4
(iii) a=2, `d=(-3)/(2)` (iv) a=-3, d=1

Answer

To find the first four terms of an Arithmetic Progression (A.P.) given the first term \( a \) and the common difference \( d \), we can use the following formula:

1. The first term \( a_1 = a \)
2. The second term \( a_2 = a + d \)
3. The third term \( a_3 = a + 2d \)
4. The fourth term \( a_4 = a + 3d \)

Now, let's solve the given parts step by step.

### (i) Given \( a = 5 \) and \( d = 3 \)

1. **First term**:
\[ a_1 = a = 5 \]
2. **Second term**:
\[ a_2 = a + d = 5 + 3 = 8 \]
3. **Third term**:
\[ a_3 = a + 2d = 5 + 2 \times 3 = 5 + 6 = 11 \]
4. **Fourth term**:
\[ a_4 = a + 3d = 5 + 3 \times 3 = 5 + 9 = 14 \]

**A.P.**: \( 5, 8, 11, 14 \)

### (ii) Given \( a = -2 \) and \( d = 4 \)

1. **First term**:
\[ a_1 = a = -2 \]
2. **Second term**:
\[ a_2 = a + d = -2 + 4 = 2 \]
3. **Third term**:
\[ a_3 = a + 2d = -2 + 2 \times 4 = -2 + 8 = 6 \]
4. **Fourth term**:
\[ a_4 = a + 3d = -2 + 3 \times 4 = -2 + 12 = 10 \]

**A.P.**: \( -2, 2, 6, 10 \)

### (iii) Given \( a = 2 \) and \( d = -\frac{3}{2} \)

1. **First term**:
\[ a_1 = a = 2 \]
2. **Second term**:
\[ a_2 = a + d = 2 - \frac{3}{2} = \frac{4}{2} - \frac{3}{2} = \frac{1}{2} \]
3. **Third term**:
\[ a_3 = a + 2d = 2 + 2 \times \left(-\frac{3}{2}\right) = 2 - 3 = -1 \]
4. **Fourth term**:
\[ a_4 = a + 3d = 2 + 3 \times \left(-\frac{3}{2}\right) = 2 - \frac{9}{2} = \frac{4}{2} - \frac{9}{2} = -\frac{5}{2} \]

**A.P.**: \( 2, \frac{1}{2}, -1, -\frac{5}{2} \)

### (iv) Given \( a = -3 \) and \( d = 1 \)

1. **First term**:
\[ a_1 = a = -3 \]
2. **Second term**:
\[ a_2 = a + d = -3 + 1 = -2 \]
3. **Third term**:
\[ a_3 = a + 2d = -3 + 2 \times 1 = -3 + 2 = -1 \]
4. **Fourth term**:
\[ a_4 = a + 3d = -3 + 3 \times 1 = -3 + 3 = 0 \]

**A.P.**: \( -3, -2, -1, 0 \)

### Summary of A.P.s:
1. \( 5, 8, 11, 14 \)
2. \( -2, 2, 6, 10 \)
3. \( 2, \frac{1}{2}, -1, -\frac{5}{2} \)
4. \( -3, -2, -1, 0 \)