Write the first six terms of an A.P. in which
a=5 ,d =4

Answer

To find the first six terms of an arithmetic progression (A.P.) where the first term \( a = 5 \) and the common difference \( d = 4 \), we can use the formula for the \( n \)-th term of an A.P.:

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

### Step-by-Step Solution:

1. **Identify the first term and common difference**:
- First term \( a = 5 \)
- Common difference \( d = 4 \)

2. **Calculate the first term \( a_1 \)**:
\[ a_1 = a = 5 \]

3. **Calculate the second term \( a_2 \)**:
\[ a_2 = a + (2 - 1) \cdot d = 5 + 1 \cdot 4 = 5 + 4 = 9 \]

4. **Calculate the third term \( a_3 \)**:
\[ a_3 = a + (3 - 1) \cdot d = 5 + 2 \cdot 4 = 5 + 8 = 13 \]

5. **Calculate the fourth term \( a_4 \)**:
\[ a_4 = a + (4 - 1) \cdot d = 5 + 3 \cdot 4 = 5 + 12 = 17 \]

6. **Calculate the fifth term \( a_5 \)**:
\[ a_5 = a + (5 - 1) \cdot d = 5 + 4 \cdot 4 = 5 + 16 = 21 \]

7. **Calculate the sixth term \( a_6 \)**:
\[ a_6 = a + (6 - 1) \cdot d = 5 + 5 \cdot 4 = 5 + 20 = 25 \]

### Summary of the First Six Terms:
- \( a_1 = 5 \)
- \( a_2 = 9 \)
- \( a_3 = 13 \)
- \( a_4 = 17 \)
- \( a_5 = 21 \)
- \( a_6 = 25 \)

Thus, the first six terms of the A.P. are: **5, 9, 13, 17, 21, 25**.