Chapter 12 - Sequences; Induction; the Binomial Theorem - 12.2 Arithmetic Sequences - 12.2 Assess Your Understanding - Page 814: 38

The common difference is: $d=4.$ The initial term: $a_1=-40.$ $a_n=4n-44$, $a_n=a_{n-1}+4$

We know that $a_{12}=4,a_{18}=28$. Thus the common difference is: $d=\frac{a_k-a_l}{k-l}=\frac{a_{18}-a_{12}}{18-12}=\frac{28-4}{6}=4.$ The initial term: $a_1=a_n-(n-1)d=a_{12}-(11)(4)=4-(11)(4)=-40.$ Thus: $a_n=a_1+(n-1)d=-40+(n-1)(4)=4n-44$, $a_n=a_{n-1}+d=a_{n-1}+4$