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If the coefficients of three consecutive terms in the expansion of ${(1 + x)}^{n}$ are in the ratio $1 : 7 : 42$ , then value of $n$ is

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Correct option is B

Let three consecutive terms be (r + 1)th, (r + 2)th and (r + 3)th. Then nCr nCr+1=17⇒r+1n−r=17⇒n−8r=7and nCr+1 nCr+2=742=16⇒r+2n−r−1=16⇒ n−7r=13|From (1) and (2), n=55.

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If the coefficients of three consecutive terms in the expansion of (1 + x)n are in the ratio 1 : 7 : 42, then value of n is

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If the coefficients of three consecutive terms in the expansion of ${(1 + x)}^{n}$ are in the ratio $1 : 7 : 42$ , then value of $n$ is