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  • If the second, third and fourth term in the expansion of  are 240,720 and 1080 respectively, t

If the second, third and fourth term in the expansion of (x+a)^n are 240,720 and 1080 respectively, then the value of n is
 

Option: 1

15


Option: 2

20


Option: 3

10


Option: 4

5


Answers (1)

best_answer

\begin{aligned} & T_2=n(x)^{n-1}(a)^1=240 \\ & T_3=\frac{n(n-1)}{1.2} x^{n-2} a^2=720 \\ & T_4=\frac{n(n-1)(n-2)}{1.2 .3} x^{n-3} {} a^3=1080 \end{aligned}\\\\ \text{To eliminate x,}\\ \begin{aligned} & \frac{T_2 \cdot T_4}{T_3^2}=\frac{240.1080}{720.720}=\frac{1}{2}=\frac{T_2}{T_3} \cdot \frac{T_4}{T_3}=\frac{1}{2} \\ & \text { Now, } \frac{T_{r+1}}{T_r}=\frac{{ }^n C_r}{{ }^n C_{r-1}}=\frac{n-r+1}{r} \end{aligned}\\\\ \text{Now, Putting r=3 and 2 in above expression, we get} \Rightarrow \frac{n-2}{3} \cdot \frac{2}{n-1}=\frac{1}{2} \Rightarrow n=5

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Rakesh

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