Question

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 :

Answer 1

We know that
`a_(n)=S_(n)-S_(n-1)`
and also,
`d=a_(n)-a_(n-1)=(S_(n)-S_(n-1))-(S_(n-1)-S_(n-2))`
`rArr d=S_(n)-2.S_(n-1)+S_(n-2)`
On comparing with `d=S_(n)-k.S_(n-1)+S_(n-2)`, we get k=2.