If `S_(n)` denotes the sum of first `n` terms of an AP, then prove that `S_(12)=3(S_(8)-S_(4)).`

Explanation

To prove that \( S_{12} = 3(S_{8} - S_{4}) \), we will use the formula for the sum of the first \( n \) terms of an arithmetic progression (AP). The formula for the sum \( S_n \) of the first \( n \) terms is given by:

\[ S_n = \frac{n}{2} \left(2a + (n - 1)d\right) \]

where \( a \) is the first term and \( d \) is the common difference.

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