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  • If the coefficient of the second, third and fourth terms in the expansion of  are in A.P., the

If the coefficient of the second, third and fourth terms in the expansion of (1+x)^n are in A.P., then n is equal to 
 

Option: 1

7


Option: 2

2


Option: 3

6


Option: 4

None of these


Answers (1)

In the expansion of (1+x)^n, it is given that { }^n C_1,{ }^n C_2,{ }^n C_3 are in A.P.

\begin{aligned} & \Rightarrow 2 \cdot{ }^n C_2={ }^n C_1+{ }^n C_3 \\ & \Rightarrow \quad 2 \cdot \frac{n(n-1)}{1 \cdot 2}=\frac{n}{1}+\frac{n(n-1)(n-2)}{1 \cdot 2 \cdot 3} \\ & \Rightarrow 6(n-1)=6+(n-2)(n-1) \\ & \Rightarrow n^2-9 n+14=0 \Rightarrow n=2 \text { or } n=7 \end{aligned}

But n = 2 is not acceptable because, when n=2, there are only three terms in the expansion of (1+x)^2, \therefore n = 7  

Posted by

Ramraj Saini

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