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  • If the coefficients of the second, third and fourth terms in the expansion of <img alt="(1+x)^n" src="https://entrancecorner.oncodecogs.com/gif.latex?%281&plus;x%29

If the coefficients of the second, third and fourth terms in the expansion of (1+x)^n are in A.P., Find n.

Option: 1

6


Option: 2

7


Option: 3

8


Option: 4

9


Answers (1)

best_answer

According to the question { }^n C_1 \cdot{ }^n C_2 \cdot{ }^n C_3 are in A.P

\frac{2 n(n-1)}{2}=n+\frac{n(n-1)(n-2)}{6} \\

n^2-9 n+14=0 \Rightarrow(n-2)(n-7)=0 \Rightarrown=2  (or) 7

Since the symbol { }^{\mathrm{n}} \mathrm{C}_3 demands that n should be \geq 3 \mathrm{n} cannot be 2,

\therefore \mathrm{n}=7 only.

Posted by

manish

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