Chapter 11 - Sequences; Induction; the Binomial Theorem - Section 11.1 Sequences - 11.1 Assess Your Understanding - Page 827: 42

$a_1= -2 \\ a_2=-4 \\ a_3=-9 \\ a_4=-23 \\ a_5=-64 $

We are given that $a_n=n+3 a_{n-1}$ and $a_1= -2$. In order to determine the remaining values, we will have to substitute $n=2,3,4,5$ into the given sequence. We use the previous terms to compute the subsequent terms as follows: $a_2=2+3 a_1=2+(3)(-2)=-4 \\ a_3=3+3 a_2=3+(3)(-4)=-9 \\ a_4=4+3 a_3=4+(3)(-9)=-23 \\ a_5=5+3 a_4=5+(3)(-23)=-64 $