The sum of m and n terms of an A.P. are n and m respectively. Prove that the sum of (m + n) terms will be - (m+n).

Explanation

To prove that the sum of (m + n) terms of an A.P. is - (m + n), given that the sum of m terms is n and the sum of n terms is m, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Given Information**:
- Let the first term of the A.P. be \( a \) and the common difference be \( d \).
- The sum of the first \( m \) terms \( S_m \) is given by:
\[
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