rth term in the expansion of (a+2x)n is

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

Options:

A .

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

B .

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

C .

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

D . None of these

Answer: Option B
:
B

$r^{t h}$ term of $(a + 2 x)^{n}$ is $^{n} C_{r - 1} (a)^{n - r + 1} (2 x)^{r - 1}$

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

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

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