Let `S_n` denote the sum of n terms of an AP whose first term is a. If common difference d is given by `d=Sn-kS_(n-1)+S_(n-2)` , then k is :

Explanation

To solve the problem, we need to find the value of \( k \) in the equation given for the common difference \( d \) of an arithmetic progression (AP). The common difference \( d \) is defined as:

\[ d = S_n - k S_{n-1} + S_{n-2} \]

where \( S_n \) is the sum of the first \( n \) terms of the AP, \( S_{n-1} \) is the sum of the first \( n-1 \) terms, and \( S_{n-2} \) is the sum of the first \( n-2 \) terms.

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