If `S_(m)=m^(2) p and S_(n)=n^(2)p`, where ` m ne n` in an AP then prove that ` S_(p) =P^(3)`

Explanation

To solve the problem, we start with the given information:

1. \( S_m = m^2 p \)
2. \( S_n = n^2 p \)

where \( m \neq n \) and both \( S_m \) and \( S_n \) represent the sums of the first \( m \) and \( n \) terms of an arithmetic progression (AP).

### Step 1: Understand the formula for the sum of the first \( n \) terms of an AP
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