Find the $r^{\text {th }}$ term from the end in the expansion of $(x+a)^{n}$
Find the $r^{\text {th }}$ term from the end in the expansion of $(x+a)^{n}$
There are $(n+1)$ terms in the expansion of $(x+a)^{n}$. Observing the terms we can say that the first term from the end is the last term, i.e., $(n+1)^{\text {th }}$ term of the expansion and $n+1=(n+1)-(1-1) .$
The second term from the end is the $n^{\text {th }}$ term of the expansion, and $n=(n+1)-(2-1) .$
The third term from the end is the $(n-1)^{\text {th }}$ term of the expansion and $n-1=(n+1)-(3-1)$ and so on.
Thus $r^{th}$ term from the end will be term number $(n+1)-(r-1)=(n-r+2)$ of the expansion. And the $(n-r+2)^{ th }$ term is $^{n} C _{n-r+1} x^{r-1} a^{n-r+1}$
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