# Trevor rides Jake piggyback III

**Calculus**Level 5

Starting at \((0,0)\), Trevor tells his serf to advance by \(\dfrac{L_{n}}{\sqrt{5}^{n}}\) meters and turn \(90^{\circ}\) clockwise at the nth step, where \(L_{1} = 1\), \(L_{2} = 3\), and \(L_{n+2} = L_{n+1}+L_{n}\).

What is the magnitude of the displacement in meters Trevor and Jake have travelled from the origin? If it is of the form \(\dfrac{a}{\sqrt[b]{c}}\) where \(a\) and \(b \geq c > 1\) are positive integers, find \(a+b+c\).