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Let Sn denote the sum of n terms of an A...

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 :

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`d = a_n - a_(n-1)`
`a_n = s_n - s_(n-1)`
`= n/2 [2a + (n-1)d] - (n-1)/2[2a + (n-2)d]`
`= (2an + n(n-1)d - (n-1)[2a+ (n-1)d])/2`
`= (2a+ (n-1)d-d +nd)/2`
`= a + nd-d`
`= a + (n-1)d`
`k=2`
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