Chapter 12 Sequences and Series - 12.2 Analyze Arithmetic Sequences and Series - 12.2 Exercises - Skill Practice - Page 807: 49

$a_n=-3+5n=5n-3$

We know that the general formula of an arithmetic sequence is given by $a_n=a_1+(n-1)d$ Here, we have $a_1=2 ; d=5$ $a_n=a_1+(n-1)d$ This gives: $a_n=2+(n-1) \times 5$ or, $a_n=2+5n-5$ Hence, $a_n=-3+5n=5n-3$