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$If S_{n} denotes the sum of first n terms of an A.P whose first term is a and \frac{S_{n x}}{S_{x}} is independent of x, then S_{ρ} =$

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Correct option is B

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

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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=

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$If S_{n} denotes the sum of first n terms of an A.P whose first term is a and \frac{S_{n x}}{S_{x}} is independent of x, then S_{ρ} =$