Chapter 12 Sequences and Series - 12.2 Analyze Arithmetic Sequences and Series - 12.2 Exercises - Skill Practice - Page 807: 51

$a_n=-2n-1$

We know that the general formula of an arithmetic sequence is given by $a_n=a_1+(n-1)d$ Here, we have $d=-3$ Here, the difference between two successive terms is $-2$. $a_n=-2n+c$ This gives: $a_1=-2+c=-3$ or, $c=-1$ Hence, $a_n=-2n-1$