Chapter 12 Sequences and Series - 12.2 Analyze Arithmetic Sequences and Series - 12.2 Exercises - Skill Practice - Page 807: 30

$a_n=-5 +9n$

We know that the general formula of an arithmetic sequence is given by $a_n= a_1+(n-1) d$ ...(1) Here, we have $a_{4}=31$ $a_{10}=a_4+6d=85$ This gives: $d=9$ $a_1=a_4-3d=31 -3 \times 9=4$ Now, $a_n=4+(n-1)9=-5+9n$ Hence, our answer is $a_n=-5 +9n$