If the first term of an A.P. is p and its common difference is q. then find its 6th term.

Answer

To find the 6th term of an Arithmetic Progression (A.P.) where the first term is \( p \) and the common difference is \( q \), we can use the formula for the \( n \)-th term of an A.P., which is given by:

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

Where:
- \( a_n \) is the \( n \)-th term,
- \( a \) is the first term,
- \( d \) is the common difference,
- \( n \) is the term number.

### Step-by-Step Solution:

1. **Identify the first term and common difference:**
- The first term \( a = p \)
- The common difference \( d = q \)

2. **Determine the term number for the 6th term:**
- Here, \( n = 6 \)

3. **Substitute the values into the formula:**
\[ a_6 = p + (6 - 1) \cdot q \]

4. **Simplify the expression:**
\[ a_6 = p + 5q \]

5. **Final answer:**
The 6th term of the A.P. is:
\[ a_6 = p + 5q \]