Question

Find the rth term from the end in the expansion of (x+a)^n

Answer 1

$\textbf{Heya Mate}$

$\textbf{Here is your answer }$

The expansion is ${(x+a)} ^ {n}$

$\textbf{Now}$

If the power is n then the number of terms be
n+1

Thus the rth term from the end of the expansion is =

Tn+1-r

= nCn+1-r × ${x}^{n-n-1+r}$ × ${a}^{n+1-r}$

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

$\textbf{Hope this helps you }$
$\textbf{Be Brainly}$

Answer 2

Answer:

$^nC_{n-r+1}.x^{r+1}.a^{n-r+1}$

Step-by-step explanation:

We know  that,

$(x+a)^n=^nC_0a^0+^nC_1\;x^{n-1}a^1...............^nC_r\;x^{n-r}a^r...........^nC_n\;x^0a^n$

There are n+1 terms  in this  expansion, and the (r+1)the  term is  given by

$T_{r+1}=^nC_r\;x^{n-r}a^r$

the rth term from the end is  = ((n+1)-r+1) =(r-r+2)th term from the starting

$\text{rth term from the end}=T_{n-r+2}\\\;\\=T_{(n-r+1)+1}\\\;\\=^nC_{n-r+1}.x^{n-n+r-1}.a^{n-r+1}\\\;\\=^nC_{n-r+1}.x^{r+1}.a^{n-r+1}$