Chapter 12 Sequences and Series - 12.2 Analyze Arithmetic Sequences and Series - 12.2 Exercises - Skill Practice - Page 807: 32

$a_n=3n-11$

We know that the general formula of an arithmetic sequence is given by $a_n= a_1+(n-1) d$ ...(1) Here, we have $d=3$; $a_3=-2; a_{17}=40$ $a_{17}=a_3+(17-3)d$ Now, we have $a_n=a_3+(n-3)d$ This gives: $a_n=-2+(n-3)3=-2+3n-9$ Hence, our answer is $a_n=3n-11$