Given that n is a positive integer and in the expansion of (1+ax)n, the coefficient of x is 200. Find the coefficient of x in the expansion of (1+ax)2n.

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$+ a x)^{n} :$

$\dbinom{n}{1}(ax)(1)^{n-1}=nax=200x$

$na=200$

$(1+ax)^{2n}:$

$\dbinom{2n}{1}(ax)(1)^{2n-1}=2nax=2(200)x=400x$

The coefficient of $x$ in the expansion of $(1+ax)^{2n}$ is $400.$

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