Question

Find the $r^{th}$ term from the end in the expansion of $(x+a{)}^n$.

• A. ${}^n{C}_r{x}^{r-1}{a}^r$
• B. ${}^n{C}_r{x}^r{a}^{n-r}$
• C. ${}^n{C}_{n-1}x{a}^{n-1}$
• D. ${}^n{C}_{n-r+1}{x}^{r-1}{a}^{n-r+1}$

Answer 1

Answer: (D)

$r^{th}$ term from the end in the expansion of $(x+a{)}^n$ is $(n-r+2{)}^{th}$ term from beginning.
$\therefore T_{\left(n-r+1\right)+1}{=}^n{C}_{n-r+1}{x}^{r-1}{a}^{n-r+1}$