[tex]a_1=\sqrt2\\a_2=2\sqrt2-2\\\\q=\frac{a_2}{a_1}=\frac{2\sqrt2-2}{\sqrt2}=\frac{2\sqrt2-2}{\sqrt2}*\frac{\sqrt2}{\sqrt2}=\frac{4-2\sqrt2}{2}=2-\sqrt2\\\\a_3=a_2*q\\a_3=(2\sqrt2-2)(2-\sqrt2)=4\sqrt2-4-4+2\sqrt2=6\sqrt2-8\\\\a_4=a_3*q\\a_4=(6\sqrt2-8)(2-\sqrt2)=12\sqrt2-12-16+8\sqrt2=20\sqrt2-28[/tex]
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[tex]a_1=\sqrt2\\a_2=2\sqrt2-2\\\\q=\frac{a_2}{a_1}=\frac{2\sqrt2-2}{\sqrt2}=\frac{2\sqrt2-2}{\sqrt2}*\frac{\sqrt2}{\sqrt2}=\frac{4-2\sqrt2}{2}=2-\sqrt2\\\\a_3=a_2*q\\a_3=(2\sqrt2-2)(2-\sqrt2)=4\sqrt2-4-4+2\sqrt2=6\sqrt2-8\\\\a_4=a_3*q\\a_4=(6\sqrt2-8)(2-\sqrt2)=12\sqrt2-12-16+8\sqrt2=20\sqrt2-28[/tex]