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 formulas:

1. First term: \( A_1 = a \)
2. Second term: \( A_2 = a + d \)
3. Third term: \( A_3 = a + 2d \)
4. Fourth term: \( A_4 = a + 3d \)

Now, let's solve the problem step by step for each part.

### (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**:
\[ A_4 = a + 3d = 5 + 3 \times 3 = 5 + 9 = 14 \]

**First four terms**: \( 5, 8, 11, 14 \)

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### (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**:
\[ A_4 = a + 3d = -2 + 3 \times 4 = -2 + 12 = 10 \]

**First four terms**: \( -2, 2, 6, 10 \)

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

1. **First term**:
\[ A_1 = a = 2 \]
2. **Second term**:
\[ A_2 = a + d = 2 - \frac{3}{2} = 2 - 1.5 = 0.5 \]
3. **Third term**:
\[ A_3 = a + 2d = 2 + 2 \times \left(-\frac{3}{2}\right) = 2 - 3 = -1 \]
4. **Fourth term**:
\[ A_4 = a + 3d = 2 + 3 \times \left(-\frac{3}{2}\right) = 2 - 4.5 = -2.5 \]

**First four terms**: \( 2, 0.5, -1, -2.5 \)

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### (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**:
\[ A_4 = a + 3d = -3 + 3 \times 1 = -3 + 3 = 0 \]

**First four terms**: \( -3, -2, -1, 0 \)

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### Summary of Results
1. For \( a = 5, d = 3 \): \( 5, 8, 11, 14 \)
2. For \( a = -2, d = 4 \): \( -2, 2, 6, 10 \)
3. For \( a = 2, d = -\frac{3}{2} \): \( 2, 0.5, -1, -2.5 \)
4. For \( a = -3, d = 1 \): \( -3, -2, -1, 0 \)

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