# Hard Sequence of Fractions

**Algebra**Level 3

\({\frac{6}{3}, \frac{18}{21}, \frac{m}{n}, \frac{32}{67}, \frac{42}{99}, \frac{a}{b}}\)

\({m}\) \(\in\) {m is a positive integer | \({\frac{1}{3}(m(4-\frac{1}{3})+(\frac{1}{4})^{-\frac{3}{2}}) = 32}\)}

\({n}\) \(\in\) {n is a prime, positive integer | \({39 < n < 51}\)}

The fraction \({\frac{a}{b}}\) is the 6th term, it is in its simplest form.

**Find the value of \({a+b}\).**