The common difference of an A.P. 6, then `a_(15) - a_(11)`…….. .

Answer

To solve the problem, we need to find the difference between the 15th term and the 11th term of an arithmetic progression (A.P.) where the common difference (d) is given as 6.

### Step-by-Step Solution:

1. **Identify the formula for the nth term of an A.P.**:
The nth term of an arithmetic progression can be expressed as:
\[ a_n = a + (n - 1)d \]
where \( a \) is the first term, \( d \) is the common difference, and \( n \) is the term number.

2. **Calculate the 15th term (a₁₅)**:
Using the formula for the nth term:
\[ a_{15} = a + (15 - 1)d = a + 14d \]

3. **Calculate the 11th term (a₁₁)**:
Similarly, for the 11th term:
\[ a_{11} = a + (11 - 1)d = a + 10d \]

4. **Find the difference (a₁₅ - a₁₁)**:
Now, we need to find the difference between the 15th term and the 11th term:
\[ a_{15} - a_{11} = (a + 14d) - (a + 10d) \]
Simplifying this, we get:
\[ a_{15} - a_{11} = a + 14d - a - 10d = 14d - 10d = 4d \]

5. **Substitute the value of d**:
We are given that the common difference \( d = 6 \):
\[ a_{15} - a_{11} = 4d = 4 \times 6 = 24 \]

### Final Answer:
Thus, the value of \( a_{15} - a_{11} \) is \( 24 \).

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