Question

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

• A. 8
• B. 9
• C. 10
• D. 11

Answer 1

Answer: (B), (C), (D)

The correct options are
B

9

C

10

D

11

There can be two cases; n is even and n is odd

If n is even, then there will be only one middle term, which is $(\frac{n+2}{2}{)}^{th}$ term.

$\frac{n+2}{2}=6$

$\Rightarrow$ n+2 = 12

$\Rightarrow$ n = 10

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 those 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