If the sum of first `m` terms of an A.P. is the same as the sum of its first `n` terms, show that the sum of tis `(m+n)` terms is zero.

Explanation

To solve the problem, we need to show that if the sum of the first \( m \) terms of an arithmetic progression (A.P.) is equal to the sum of the first \( n \) terms, then the sum of the first \( m+n \) terms is zero.

### Step-by-Step Solution:

1. **Write the formula for the sum of the first \( m \) terms of an A.P.**:
The sum of the first \( m \) terms, denoted as \( S_m \), is given by:
\[
S_m = \frac{m}{2} \left(2a + (m-1)d\right)
...