Question

Find the middle term(s) in the expansion of $(a+b{)}^{21}$

• A.
• B.
• C.
• D.

Answer 1

Answer: (A), (B)

The correct options are
A

B

In the expansion of $(a+b{)}^n$,if n is odd, there are two are two middle terms, which are $(\frac{n+1}{2}{)}^{th}$ and $(\frac{n+1}{2}+1{)}^{th}$ terms.

In this case, n = 21. The middle terms are $(\frac{21+1}{2}{)}^{th}$ and $(\frac{21+1}{2}+1{)}^{th}$ terms or

${11}^{th}and{12}^{th}$ term

$T_{11}=T_{10+1}={}^{21}{C}_{10}{a}^{21-10}{b}^{10}$

= ${}^{21}{C}_{10}{a}^{11}{b}^{10}$

$T_{12}=T_{11+1}={}^{21}{C}_{11}{a}^{21-11}{b}^{11}$

= ${}^{21}{C}_{11}{a}^{10}{b}^{11}$