If the coefficients of ${p^{th}}$, ${(p + 1)^{th}}$ and ${(p + 2)^{th}}$ terms in the expansion of ${(1 + x)^n}$ are in $A.P.$, then

  • [AIEEE 2005]
  • A

    ${n^2} - 2np + 4{p^2} = 0$

  • B

    ${n^2} - n\,(4p + 1) + 4{p^2} - 2 = 0$

  • C

    ${n^2} - n\,(4p + 1) + 4{p^2} = 0$

  • D

    None of these

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