Chapter 12 - Sequences; Induction; the Binomial Theorem - 12.2 Arithmetic Sequences - 12.2 Assess Your Understanding - Page 814: 32

The common difference is: $d=2.$ The initial term: $a_1=-3.$ $a_n=-5+2n$, $a_n=a_{n-1}+2$

We know that $a_{4}=3,a_{20}=35$. Thus the common difference is: $d=\frac{a_k-a_l}{k-l}=\frac{a_{20}-a_{4}}{20-4}=\frac{35-3}{16}=2.$ The initial term: $a_1=a_n-(n-1)d=a_4-(3)d=3-(3)2=-3.$ Thus: $a_n=a_1+(n-1)d=-3+(n-1)2=-5+2n$, $a_n=a_{n-1}+d=a_{n-1}+2$