Question

explanation required ​

Answer 1

Let a is the first term, n is the number of terms and d is the common difference of AP.

Given d = Sn - kSn-1 + Sn-2 and we have to find the value of k.

Now let n = 3

So AP is : a , a + d, a + 2d

and d = S3 - kS3-1 + S3-2 

=>  d = S3 - kS2 + S1 ..............1

Sum of n terms of an AP is given as: 

Sn = (n/2)*{2a + (n-1)d}

Now S1 = a

       S2 = (2/2)*(2a + (2-1)d)        (n =2)

=> S2 = (2a + d)         

      S3 = (3/2)*(2a + (3-1)d)        (n =3)

=> S3 = (3/2)*(2a + 2d)

=> S3 = 3(a + d)

=> S3 = 3a + 3d

Put value of S1 , S2 and S3 in equation 1, we get

      d = 3a + 3d - k(2a + d) + a

=> d = 4a + 3d - k(2a + d)

=> k(2a + d) = 4a + 3d - d

=> k(2a + d) = 4a + 2d

=> k(2a + d) = 2(2a + d)

=> k = 2

So value of K is 2 

Answer 2

Answer:

Solving in two ways