$d={{t}_{2}}-{{t}_{1}}=(4+\sqrt{2})-(3+2\sqrt{2})=1-\sqrt{2}$  $n=\frac{{{t}_{n}}-{{t}_{1}}}{d}+1=\frac{(52-47\sqrt{2})-(3+2\sqrt{2})}{1-\sqrt{2}}+1=50$