Chapter 12 Sequences and Series - 12.2 Analyze Arithmetic Sequences and Series - 12.2 Exercises - Skill Practice - Page 806: 29

$C$ ; $a_n=-63 +4n$

We know that the general formula of an arithmetic sequence is given by $a_n= a_1+(n-1) d$ ...(1) Here, we have $a_{30}=57; d=4$ $57=a_1+(30-1) \times (4)$ This gives: $57=a_1+116$ or, $a_1=-59$ Now, $a_n=-59+(n-1)4=-63 +4n$ Hence, our answer is $C$ ; $a_n=-63 +4n$