Let Sn denote the sum of n terms of an A.P. whose first term is a. If

1.	Let Sn denote the sum of n terms of an A.P. whose first term is a. If the common difference d is given by d = Sn - k Sn-1 + Sn-2, then k =A. 1 B. 2 C. 3 D. none of these
Answer» Option : (B) We know, S_n = S_n-2+a_n-1+a_n = S_n-2+a+(n-2)d+a+(n-1)d = S_n-2+2a+2nd-3d Also, S_n-1= S_n-2+a_n-1 = S_n-2+a+(n-2)d = S_n-2+a+nd-2d Now, d = S_n-kS_n-1+S_n-2 = S_n-2+2a+2nd-3d-k(S_n-2+a+nd-2d)+S_n-2 = (2-k)[S_n-2+a+nd]+d(2k-3) Comparing coefficient of both the side we get, 2-k = 0 and 2k-3 =1 ∴ k = 2

Let Sn denote the sum of n terms of an A.P. whose first term is a. If the common difference d is given by d = Sn - k Sn-1 + Sn-2, then k =A. 1 B. 2 C. 3 D. none of these

Answer»

Option : (B)

We know,

S_n = S_n-2+a_n-1+a_n

= S_n-2+a+(n-2)d+a+(n-1)d

= S_n-2+2a+2nd-3d

Also,

S_n-1= S_n-2+a_n-1

= S_n-2+a+(n-2)d

= S_n-2+a+nd-2d

Now,

d = S_n-kS_n-1+S_n-2

= S_n-2+2a+2nd-3d-k(S_n-2+a+nd-2d)+S_n-2

= (2-k)[S_n-2+a+nd]+d(2k-3)

Comparing coefficient of both the side we get,

2-k = 0 and 2k-3 =1

∴ k = 2