Chapter 12 - Sequences; Induction; the Binomial Theorem - 12.2 Arithmetic Sequences - 12.2 Assess Your Understanding - Page 814: 34

The common difference is: $d=-10.$ The initial term: $a_1=74.$ $a_n=84-10n$, $a_n=a_{n-1}-10$

We know that $a_{8}=4,a_{18}=-96$. Thus the common difference is: $d=\frac{a_k-a_l}{k-l}=\frac{a_{18}-a_{8}}{18-8}=\frac{-96-4)}{10}=-10.$ The initial term: $a_1=a_n-(n-1)d=a_8-(7)(-10)=4-(7)(-10)=74.$ Thus: $a_n=a_1+(n-1)d=74+(n-1)(-10)=84-10n$, $a_n=a_{n-1}+d=a_{n-1}-10$