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.
$\therefore T_{\left(n-r+1\right)+1} = ^{n}C_{n-r+1}\,x^{r-1}\,a^{n-r+1}$