Question

The middle term of the binomial expansion of $(a+b{)}^n$ is the $6^{th}$ term. Find the possible values of n, if n is odd.

• A. 8
• B. 9
• C. 10
• D. 11

Answer 1

Answer: (B), (D)

The correct options are
B

9

D

11

If n is odd, there will be two middle terms which are $(\frac{n+1}{2}{)}^{th}$ and $(\frac{n+1}{2}+1{)}^{th}$

terms.

6 can be any of these values

$\Rightarrow \frac{n+1}{2}=6$ or $\frac{n+1}{2}+1=6$

$\Rightarrow$ n + 1 = 12 or n + 1 = 10

$\Rightarrow$ n = 11 or n = 9