For some $n
eq10$, let the coefficients of the 5th, 6th and 7th terms in the binomial expansion of $(1+x)^{n+4}$ be in A.P. Then the largest coefficient in the expansion of $(1+x)^{n+4}$ is:

Question

Dr. Abubacker · Accepted Answer

[Solution by Dr. Abubacker] Let $N=n+4$. $2\binom N5=\binom N4+\binom N6$ gives $N^2-21N+98=0$, so $N=7$ or $14$. $n
e10$ rules out $N=14$, so $N=7$ and the largest coefficient is $\binom73=35$. Answer (3).

Q. For some $n\neq10$, let the coefficients of the 5th, 6th and 7th terms in the binomial expansion of $(1+x)^{n+4}$ be in A.P. Then the largest coefficient in the expansion of $(1+x)^{n+4}$ is:

Explanation

Reviewed by Dr. Abubacker

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