Find the $r^{t h}$ term from the end in the expansion of $(x + a)^{n}$

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Solution

In the expansion of $(x + a)^{n}$
pth term from end = $T_{n - p + 2}$
Therefore, rth term from end = $T_{n - r + 2}$
$T_{n - r + 2} = {n_{C}}_{n - r + 1} (x)^{n - n + r - 1} . a^{n - r + 1}$
$= {n_{C}}_{n - r + 1} (x)^{r - 1} . a^{n - r + 1}$

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

In the expansion of (x+a)npth term from end = Tn−p+2Therefore, rth term from end = Tn−r+2Tn−r+2=nCn−r+1(x)n−n+r−1.an−r+1=nCn−r+1(x)r−1.an−r+1

Find the $r^{t h}$ term from the end in the expansion of $(x + a)^{n}$

In the expansion of $(x + a)^{n}$
pth term from end = $T_{n - p + 2}$
Therefore, rth term from end = $T_{n - r + 2}$
$T_{n - r + 2} = {n_{C}}_{n - r + 1} (x)^{n - n + r - 1} . a^{n - r + 1}$
$= {n_{C}}_{n - r + 1} (x)^{r - 1} . a^{n - r + 1}$