Chapter 11 - 11.4 - Mathematical Induction - 11.4 Exercises - Page 807: 62

See below.

$a_1=2$ $a_2=a_1+2=2+2=4$ $a_3=a_2+2=4+2=6$ $a_4=a_3+2=6+2=8$ $a_5=a_4+2=8+2=10$ $a_6=a_5+2=10+2=12$ The first differences: $a_2-a_1=a_3-a_2=a_4-a_3=a_5-a_4=a_6-a_5=2$ The second differences: $2-2=2-2=2-2=2-2=0$. The first differences are constant; thus it is linear.