Find the rth term from the end in `(x+a)^(n)`.

Answer

To find the r-th term from the end in the expansion of \((x + a)^n\), we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Binomial Expansion**:
The general term (k-th term) in the expansion of \((x + a)^n\) is given by:
\[ T_k = \binom{n}{k-1} x^{n-(k-1)} a^{k-1} \]
where \(k\) is the term number.

2. **Identify the r-th Term from the End**:
The r-th term from the end can be related to the term from the beginning. The r-th term from the end corresponds to the \((n - r + 1)\)-th term from the beginning.

3. **Substitute for k**:
Therefore, we need to find:
\[ T_{n - r + 1} = \binom{n}{(n - r + 1) - 1} x^{n - ((n - r + 1) - 1)} a^{(n - r + 1) - 1} \]
Simplifying this gives:
\[ T_{n - r + 1} = \binom{n}{n - r} x^{r} a^{n - r} \]

4. **Final Expression**:
Thus, the r-th term from the end in the expansion of \((x + a)^n\) is:
\[ T_r = \binom{n}{r-1} x^{n - (r-1)} a^{r-1} \]
which can also be expressed as:
\[ T_r = \binom{n}{n - r} x^{r} a^{n - r} \]

### Final Answer:
The r-th term from the end in \((x + a)^n\) is:
\[ T_r = \binom{n}{r-1} x^{n - (r-1)} a^{r-1} \]