If S n , denote the sum of n terms of an A.P. with first term a and common difference d such that , is independent of x, then

Question

Philoid · Accepted Answer

Given AP in which First term = a, Common difference = d, Number of terms = n

And S_n denotes the sum of n terms

So

and

Now,

If d= 2a

S_x /S_kx = (2×a) / (k²×2a)

= 1/ k²

So S_x /S_kx is independent of if d = 2a