The coefficients of 2nd, 3rd and 4th terms in the expansion of $(1 + x)^{n}$ are in A.P. then $n =$

7

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8

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9

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14

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Solution

The correct option is A $7$
Coefficient of $(r + 1)$ th in the expansion of $(1 + x)^{n}$ is $^{n} C_{r}$
Given 2nd, 3rd and 4th terms are in A.P
$\Rightarrow {2.}^{n} C_{2} =^{n} C_{1} +^{n} C_{3}$
$\Rightarrow n (n - 1) = n + \frac{n (n - 1) (n - 2)}{6}$
$\Rightarrow 6 (n - 1) = 6 + n^{2} - 3 n + 2$
$\Rightarrow n^{2} - 9 n + 14 = 0 \Rightarrow n = 7$

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