Chapter 12 - Sequences; Induction; the Binomial Theorem - 12.2 Arithmetic Sequences - 12.2 Assess Your Understanding - Page 814: 31

Thus the common difference is: $d=3.$ The initial term: $a_1=-13.$ $a_n=-16+3n$, $a_n=a_{n-1}+3$

We know that $a_{8}=8,a_{20}=44$. Thus the common difference is: $d=\frac{a_k-a_l}{k-l}=\frac{a_{20}-a_{8}}{20-8}=\frac{44-8}{12}=3.$ The initial term: $a_1=a_n-(n-1)d=a_8-(7)d=8-(7)3=-13.$ Thus: $a_n=a_1+(n-1)d=-13+(n-1)3=-16+3n$, $a_n=a_{n-1}+d=a_{n-1}+3$