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 its `(m+n)` terms is zero.

Explanation

To show that the sum of the first \( (m+n) \) terms of an arithmetic progression (A.P.) is zero, given that the sum of the first \( m \) terms is equal to the sum of the first \( n \) terms, we can follow these steps:

### Step 1: Write the formulas for the sums of the first \( m \) and \( n \) terms
The sum of the first \( m \) terms of an A.P. can be expressed as:
\[ S_m = \frac{m}{2} \left(2a_1 + (m-1)d\right) \]
Similarly, the sum of the first \( n \) terms is:
...