If a>0  and coefficient of x2, x3, x4 in the expansion of 1+xa6  are in A.P., then a equals

# If $a>0$  and coefficient of  in the expansion of ${\left(1+\frac{x}{a}\right)}^{6}$  are in $A.P.,$ then a equals

1. A

$\frac{\left(4+\sqrt{7}\right)}{3}$

2. B

$\frac{\left(4+\sqrt{3}\right)}{3}$

3. C

$2-\sqrt{3}$

4. D

$2+\sqrt{3}$

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### Solution:

Coefficient of ${x}^{r}$ in the expansion of

$\left(1+x/a{\right)}^{6}{=}^{6}{C}_{r}\left(1/a{\right)}^{\mathrm{r}}$

According to given condition

are in A.P.

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