r=a_{n+1}-a_n różnica ciągu arytmetycznego
a_1=\sqrt2+1
a_2=\frac{1}{\sqrt2+1}
a_3=\sqrt2-3
r=a_2-a_1=\frac{1}{\sqrt2+1}-(\sqrt2+1)=\frac{\sqrt2-1}{(\sqrt2+1)(\sqrt2-1)}-\sqrt2-1=
=\frac{\sqrt2-1}{2-1}-\sqrt2-1=\sqrt2-1-\sqrt2-1=-2
i
r=a_3-a_2=\sqrt2-3-\frac{1}{\sqrt2+1}=\sqrt2-3-\frac{\sqrt2-1}{(\sqrt2+1)(\sqrt2-1)}=
=\sqrt2-3-\frac{\sqrt2-1}{2-1}=\sqrt2-3-(\sqrt2-1)=\sqrt2-3-\sqrt2+1=-2
r = -2 <-- odpowiedź