Chapter 11 - Sequences; Induction; the Binomial Theorem - Section 11.2 Arithmetic Sequences - 11.2 Assess Your Understanding - Page 834: 30

$d=2$. $a_1= -3$, $a_n= a_{n-1}+2$. $a_n= 2n-5$

1. Based on the given conditions, we have $a_4=a_1+3d=3$ and $a_{20}=a_1+19d=35$, thus $16d=32$ and $d=2$. 2. We can find the first term $a_1=3-3(2)=-3$, and a recursive formula $a_n=a_{n-1}+d=a_{n-1}+2$. 3. We can find a formula for the nth term $a_n=a_1+(n-1)d=--3+(n-1)2=2n-5$