The first term of an AP is p and the common difference is q, then its 20th term is

Options

A. q +19p
B. p - 9q
C. p + 19q
D. 2p + 9q

Answer

To find the 20th term of an arithmetic progression (AP) where the first term is \( p \) and the common difference is \( q \), we can follow these steps:

### Step-by-Step Solution:

1. **Understand the formula for the nth term of an AP:**
The nth term of an arithmetic progression can be calculated using the formula:
\[ A_n = A + (n - 1)D \]
where \( A \) is the first term, \( D \) is the common difference, and \( n \) is the term number.

2. **Identify the values for this problem:**
In this case, the first term \( A = p \) and the common difference \( D = q \). We want to find the 20th term, so \( n = 20 \).

3. **Substitute the values into the formula:**
We substitute \( A \), \( D \), and \( n \) into the formula:
\[ A_{20} = p + (20 - 1)q \]

4. **Simplify the expression:**
Now, simplify the expression:
\[ A_{20} = p + 19q \]

5. **Final result:**
Therefore, the 20th term of the AP is:
\[ A_{20} = p + 19q \]