Chapter 11 - Further Topics in Algebra - 11.2 Arithmetic Sequences and Series - 11.2 Exercises - Page 1024: 22

$a_1=3-\sqrt{2}$ $a_2=3$ $a_3=3+\sqrt{2}$ $a_4=3+2\sqrt{2}$ $a_5=3+3\sqrt{2}$

$a_1=3-\sqrt{2}$ $a_2=3$ Determine the common difference $d$: $d=a_2-a_1=3-(3-\sqrt{2})=\sqrt{2}$ Then we have: $a_3=a_2+d=3+\sqrt{2}$ $a_4=a_3+d=(3+\sqrt{2})+\sqrt{2}=3+2\sqrt{2}$ $a_5=a_4+d=(3+2\sqrt{2})+\sqrt{2}=3+3\sqrt{2}$