Chapter 12 - Sequences; Induction; the Binomial Theorem - 12.2 Arithmetic Sequences - 12.2 Assess Your Understanding - Page 814: 36

The common difference is: $d=4.$ The initial term: $a_1=-18.$ $a_n=4n-22$, $a_n=a_{n-1}+4$

We know that $a_{5}=-2,a_{13}=30$. Thus the common difference is: $d=\frac{a_k-a_l}{k-l}=\frac{a_{13}-a_{5}}{13-5}=\frac{30-(-2)}{8}=4.$ The initial term: $a_1=a_n-(n-1)d=a_{2}-(4)(4)=-2-(4)(4)=-18.$ Thus: $a_n=a_1+(n-1)d=-18+(n-1)(4)=4n-22$, $a_n=a_{n-1}+d=a_{n-1}+4$