Mark the correct alternative in the following: Let denote the sum of n terms of an A.P. whose first term is a. If the common difference d is given by , then k =

Question

Philoid · Accepted Answer

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

Mark the correct alternative in the following:Let denote the sum of n terms of an A.P. whose first term is a. If the common difference d is given by , then k =

Mark the correct alternative in the following:
Let denote the sum of n terms of an A.P. whose first term is a. If the common difference d is given by , then k =