If Sn denotes the sum of first n terms of an A.P whose first term is a and SnxSx is independent of x, then Sρ=

SnxSx=nx2[2a+(nx−1)d]x2[2a+(x−1)d]  =n[(2a−d)+nxd](2a−d)+xd For SnxSx to be independent of x, 2a−d=0⇒2a=d Now, Sp=p2[2a+(p−1)d]=p2a