Question

$r^{th}$ term in the expansion of $(a+2x{)}^n$ is

• A. $\frac{n(n+1).....(n-r+1)}{r!}{a}^{n-r+1}(2x{)}^r$
• B. $\frac{n(n-1).....(n-r+2)}{(r-1)!}{a}^{n-r+1}(2x{)}^{r-1}$
• C. $\frac{n(n+1).....(n-r)}{(r+1)!}{a}^{n-r}\left(x\right)r$
• D. None of these

Answer 1

The correct option is B

$\frac{n(n-1).....(n-r+2)}{(r-1)!}{a}^{n-r+1}(2x{)}^{r-1}$

$r^{th}$ term of $(a+2x{)}^n$ is ${}^n{C}_{r-1}\left(a{)}^{n-r+1}\right(2x{)}^{r-1}$

= $\frac{n!}{(n-r+1)!(r-1)!}{a}^{n-r+1}(2x{)}^{r-1}$

= $\frac{n(n-1).....(n-r+2)}{(r-1)!}{a}^{n-r+1}(2x{)}^{r-1}$