Write the first six terms of an A.P. in which
a=x ,d = 3x +2

Answer

To find the first six terms of an Arithmetic Progression (A.P.) where the first term \( a = x \) and the common difference \( d = 3x + 2 \), we can follow these steps:

### Step 1: Identify the first term and common difference
Given:
- First term \( a = x \)
- Common difference \( d = 3x + 2 \)

### Step 2: Write the formula for the nth term of an A.P.
The nth term of an A.P. can be calculated using the formula:
\[ a_n = a + (n - 1) \cdot d \]
where \( a_n \) is the nth term, \( a \) is the first term, \( d \) is the common difference, and \( n \) is the term number.

### Step 3: Calculate the first six terms
Using the formula, we can calculate the first six terms:

1. **First term** \( a_1 \):
\[ a_1 = a = x \]

2. **Second term** \( a_2 \):
\[ a_2 = a + d = x + (3x + 2) = 4x + 2 \]

3. **Third term** \( a_3 \):
\[ a_3 = a + 2d = x + 2(3x + 2) = x + 6x + 4 = 7x + 4 \]

4. **Fourth term** \( a_4 \):
\[ a_4 = a + 3d = x + 3(3x + 2) = x + 9x + 6 = 10x + 6 \]

5. **Fifth term** \( a_5 \):
\[ a_5 = a + 4d = x + 4(3x + 2) = x + 12x + 8 = 13x + 8 \]

6. **Sixth term** \( a_6 \):
\[ a_6 = a + 5d = x + 5(3x + 2) = x + 15x + 10 = 16x + 10 \]

### Final Result
The first six terms of the A.P. are:
1. \( x \)
2. \( 4x + 2 \)
3. \( 7x + 4 \)
4. \( 10x + 6 \)
5. \( 13x + 8 \)
6. \( 16x + 10 \)