2016 VS AM P1 Q4

In the expansion of \({{\left( ax+\frac{1}{x} \right)}^{n}}\) in descending powers of \(x\), where \(a\) and \(n\) are positive integers, the fourth term of the expansion is the constant term.

1. Find the value of \(n\) and hence, express the constant term in terms of \(a\).[4]
2. Using your value of \(n\) in (i), determine if a term in \(\frac{1}{{{x}^{3}}}\) in the expansion \(\left( 1-x \right){{\left( ax+\frac{1}{x} \right)}^{n}}\) exists.[2]