Question

Let S_n denote the sum of n terms of an A.P. whose first term is a. If the common difference d is given by d = S_n − kS_n−1 + S_n−2, then k =

(a) 1

(b) 2

(c) 3

(d) none of these.

Answer 1

In the given problem, we are given

We need to find the value of k

So here,

First term = a

Common difference = d

Sum of n terms = S_n

Now, as we know,

Also, for n-1 terms,

Further, for n-2 terms,

Now, we are given,

Using (1), (2) and (3) in the given equation, we get

Taking common, we get,

Taking 2 common from the numerator, we get,

Therefore,

Hence, the correct option is (b).