Question

The common difference of an A.P., the sum of whose n terms is S_n, is

(a) S_n − 2S_n−1 + S_n−2

(b) S_n − 2S_n−1 − S_n−2

(c) S_n − S_n−2

(d) S_n − S_n−1

Answer 1

Here, we are given an A.P. the sum of whose n terms is S_n. So, to calculate the common difference of the A.P, we find two consecutive terms of the A.P.

Now, the n^th term of the A.P will be given by the following formula,

Next, we find the (n − 1)^th term using the same formula,

Now, the common difference of an A.P. (d) =

Therefore,

Hence the correct option is (a).